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Chapter 2: Q6. (page 52)

Two supplementary angles are congruent. Find their measures.

Short Answer

Expert verified

The measures of two supplementary angles that are congruent are 90 and 90.

Step by step solution

01

Step 1. Definition of supplementary angles.

The supplementary angles are the angles whose sum is 180.

02

Step 2. Definition of congruent angles.

The two angles are said to be congruent angles if they have equal measure.

03

Step 3. Write the relations between the angles A and B.

Consider the two supplementary angles that are congruent be鈭�A and 鈭�B.

As the angles鈭�A and鈭�B are supplementary angles.

Therefore,

鈭�A+鈭�B=1801.

As the angles鈭�A and鈭�B are congruent angles.

Therefore,

鈭�A=鈭�B2

04

Step 4. Solve the equations (1) and (2) by substituting A for B into the equation (1).

鈭�A+鈭�B=180鈭�A+鈭�A=1802鈭�A=180鈭�A=1802鈭�A=90

Therefore, the value of the angle鈭�A is 90.

05

Step 5. Find the value of B.

鈭�B=鈭�A=90

Therefore, the value of the angle鈭�B is 90.

06

Step 6. Write the measures of the two supplementary angles that are congruent.

The measures of the two supplementary angles that are congruent are 90 and 90.

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Most popular questions from this chapter

Cut the Mobius band lengthwise down the middle. (Start at a point midway between the edges and cut around the band.) What is the result? Cut the band a second time down the middle. Write a sentence or two describing what happens.

Can you conclude from the information given for the exercise that XY鈫�鈯�XZ鈫�?

鈭�1and鈭�3 are complementary.

a. Are there any angles in the diagram that must be congruent to鈭�4? Explain.

b. If 鈭�4 and 鈭�5 are supplementary, name all angles shown that must be congruent to 鈭�4.

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.

If points D, E, and F are collinear, then DE+EF=DF.

What can you conclude if the following sentences are all true?

  1. If(1) p, then q.
  2. (2) p
  3. I(3) q, then not r.

(4) s or r
See all solutions

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