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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

State the hypothesis and the conclusion of each conditional.

If , then .

Provide a counterexample to show that each statement is false.

Statement: If point G is on AB鈫�,then G is onBA鈫�.

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

Statement: If m鈭�T=40then 鈭�Tis not obtuse.

State the hypothesis and the conclusion of each conditional.

If , then .

Justify each step.

15y+7=12鈭�20y

35y+7=12

35y=5

y=17
See all solutions

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