Mathematics

△abc has a b c. if one of the angles in the triangle is 60°, name the angle that can be equal to 90°.

Step-by-step answer

**P** Answered by Master 1

The angle that can be equal to 90° will be or

Step-by-step explanation:

has .

That means, the longest side is and the shortest side is

As the sum of all angles in a triangle is 180°, then if two angles are 60° and 90°, so the third angle will be:

Now, we know that the measure of opposite angle to the longest side is the largest angle.

As here side is the longest side, so or will be the largest angle which is 90°

Mathematics

△abc has a b c. if one of the angles in the triangle is 60°, name the angle that can be equal to 90°.

Step-by-step answer

**P** Answered by PhD 7

∠A = 90°

Step-by-step explanation:

In this question relation between angles a, b and c have been given.

If one angle is 60° then we have to find the angle which measure 90°.

In triangle ABC,

∠A + ∠B + ∠C = 180°

If angle B = 60°

Then ∠A + 60 + ∠C = 180

∠A + ∠C = 180 - 60

∠A + ∠C = 120°

We know ∠A > ∠C

Therefore, ∠A = 90°

and ∠C = 30°

Now the angles of the triangle will be

∠A = 90°

∠B = 60°

∠C = 30°

∠A = 90° will be the answer.

Mathematics

1)triangle abc has the angle measures shown.measure of angle a = (2 x) degrees. measure of angle b = (3 x) degrees. measure of angle c = (4 x) degrees.which statement is true about the angles? measure of angle a = 20 degreesmeasure of angle b = 60 degreesangle a and angle b are complementarymeasure of angle a + measure of angle c = 100 degrees2)if a translation of is applied to square abcd, what is the y-coordinate of b ? -12-8-6-23)which value of x would make line segment n o is parallel to line segment k j? 168104)the proof that δabc ≅ δcda is

Step-by-step answer

**P** Answered by PhD 14

Which statement is true about the angles? Answer is measure B is = 60 which is B

Step-by-step explanation:

took the test

Mathematics

Triangle A B C is a rotation of triangle ABC by 60 degrees using Q as the center. Select ALL statements that MUST be true. -Angle ABC is 60 degrees. -Angle AQA is 60 degrees. -Points C and C coincide. -Triangles ABC and A B C are congruent. -Angle ABC is congruent to angle A B C -Segment BC is congruent to segment B C -Segment BQ is congruent to segment C Q. -Segment AQ is congruent to segment A Q.

Step-by-step answer

**P** Answered by PhD 10

9514 1404 393

see below

Step-by-step explanation:

When a figure is rotated about a center point, the central angle formed by any point on the figure and the corresponding image point will be the rotation angle. Every image point is the same distance from the center of rotation that the pre-image point was. No lengths or angles are changed: rotation is a "rigid motion", so the rotated figure is congruent with the original.

__

-Angle AQA' is 60 degrees.

-Triangles ABC and A'B'C' are congruent.

-Angle ABC is congruent to angle A'B'C'. (this is one of the angles of the congruent triangles)

-Segment BC is congruent to segment B'C'

-Segment AQ is congruent to segment A'Q.

Mathematics

Triangle A B C is a rotation of triangle ABC by 60 degrees using Q as the center. Select ALL statements that MUST be true. * A. Angle ABC is 60 degrees. B. Angle AQA is 60 degrees. C. Points C and C coincide. D. Triangles ABC and A B C are congruent. E. Angle ABC is congruent to angle A B C F. Segment BC is congruent to segment B C G. Segment BQ is congruent to segment C Q. H.Segment AQ is congruent to segment A Q.

Step-by-step answer

**P** Answered by PhD 4

The correct options are;

D. Triangles ABC and A'B'C' are congruent

E. Angle ABC is congruent to angle A'B'C'

F. Segment BC is congruent to segment B'C'

H. Segment AQ is congruent to segment A'Q'

Step-by-step explanation:

The given information are;

The angle of rotation of triangle ABC = 60°

Therefore, given that a rotation of a geometric figure about a point on the coordinate plane is a form of rigid transformation, we have;

1) The length of the sides of the figure of the preimage and the image are congruent

Therefore;

BC ≅ B'C'

2) The angles formed by the sides of the preimage are congruent to the angles formed by the corresponding sides of the image

Therefore;

∠ABC ≅ ∠A'B'C'

3) The distances of the points on the figure of the preimage from the coordinates of the point of rotation are equal to the distances of the points on the figure of the image from the coordinates of the point of rotation

Therefore;

Segment AQ ≅ A'Q'.

Mathematics

Triangle a b c is shown with its exterior angles. line c b extends through point d. line b c extends to form exterior angle that is 135 degrees. angle c a b is 75 degrees. what is m∠abc? m∠abc = 15° m∠abc = 45° m∠abc = 60° m∠abc = 75°

Step-by-step answer

**P** Answered by PhD 39

m∠ABC = 45°

Step-by-step explanation:

See the attached figure.

As shown in the figure

Line C B extends through point D to form the exterior angle that is 135 degrees.

So, m∠ABD = 135°

But m∠ABC + m∠ABD = 180°

∴m∠ABC = 180° - m∠ABD = 180° - 135°= 45°

Also, we should know that

m∠ABD = m∠BAC + m∠ACB

So, m∠ACB = 135° - 75° = 60°

========================================

Very important note:

If we replaced the location of B and C

SO, m∠ABC = 60° and m∠ACB = 45°

=========================================

Mathematics

Drag a statement or reason to each box to complete this proof. given: the measure of angle a c d equals 60 degrees. prove: triangle a b c is an obtuse triangle. art: a triangle a b c. side b c of the triangle is extended as a ray through point d. statements reasons 1. m∠acd=60° given 2. ∠acd and ∠acb are supplementary. 3. m∠acd+m∠acb=180° definition of supplementary angles 4. substitution property of equality 5. subtraction property of equality 6. ∠acb is an obtuse angle. 7. △abc is an obtuse triangle. definition of obtuse triangle a. m∠acb=120°

Step-by-step answer

**P** Answered by PhD 38

1. m∠ACD=60° Given

2. ∠ACD and ∠ACB are supplementary Linear Pair Postulate

3. m∠ACD+m∠ACB=180° Definition of supplementary angles

4. 60°+m∠ACB=180° (Substitute 60° on the place of m∠ACD) Substitution property of equality

[The substitution property of equality says that if a=b, then 'a' can be substituted in for 'b' in any equation or vice versa]

5. m∠ACB=120° [Subtract 60° from the both sides] Subtraction Property of Equality

[Subtraction property of equality says that if we subtract from one side of an equation,then it must be subtracted from the other side of the equation to keep the equation the same.]

6. ∠ACB is an obtuse angle. Definition of obtuse angle

[An obtuse angle is an angle of greater than 90° and less than 180°.]

7. △ABC is an obtuse triangle. Definition of obtuse triangle

Mathematics

Drag a statement or reason to each box to complete this proof. given: the measure of angle a c d equals 60 degrees. prove: triangle a b c is an obtuse triangle. art: a triangle a b c. side b c of the triangle is extended as a ray through point d. statements reasons 1. m∠acd=60° given 2. ∠acd and ∠acb are supplementary. 3. m∠acd+m∠acb=180° definition of supplementary angles 4. substitution property of equality 5. subtraction property of equality 6. ∠acb is an obtuse angle. 7. △abc is an obtuse triangle. definition of obtuse triangle a. m∠acb=120°

Step-by-step answer

**P** Answered by PhD 38

1. m∠ACD=60° Given

2. ∠ACD and ∠ACB are supplementary Linear Pair Postulate

3. m∠ACD+m∠ACB=180° Definition of supplementary angles

4. 60°+m∠ACB=180° (Substitute 60° on the place of m∠ACD) Substitution property of equality

[The substitution property of equality says that if a=b, then 'a' can be substituted in for 'b' in any equation or vice versa]

5. m∠ACB=120° [Subtract 60° from the both sides] Subtraction Property of Equality

[Subtraction property of equality says that if we subtract from one side of an equation,then it must be subtracted from the other side of the equation to keep the equation the same.]

6. ∠ACB is an obtuse angle. Definition of obtuse angle

[An obtuse angle is an angle of greater than 90° and less than 180°.]

7. △ABC is an obtuse triangle. Definition of obtuse triangle

Mathematics

me asap will mark brainliest, , and rate 5 stars if correct question what is the measure of angle ced? there are two triangles labeled abc and dce with a common vertex c. in triangle abc, angle bac is labeled as m, and angle abc is labeled as 60 degrees. in triangle dce, angle cde is labeled as 60 degrees. answer choices a. m, because triangle abc is similar to triangle edc b. m over 2, because triangle abc is congruent to triangle dce c. m + 60 degrees, because triangle abc is similar to triangle dce d. 120 degrees − m, because triangle abc is

Step-by-step answer

**P** Answered by Specialist 1

x =m

hi see this answer

Mathematics

Triangle A B C is a reflection of triangle ABC across the line I. Select ALL statements that MUST be true. * -Line I bisects segment AB. - Line I bisets segment CC . -Angle ABC is 60 degrees. -Line BB is perpendicular to line I. -Angle ABC is congruent to angle A B C . -Triangle ABC and A B C are congruent. -Segment BC is congruent to segment B C . -The distance from point A to line I is the same as the distance from point A to line 1.

Step-by-step answer

**P** Answered by Specialist 9

Step-by-step explanation:

x- axis is 2 units away