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Chapter 3: Q3. (page 82)

For each statement

  1. tell whether the statement is true or false,
  2. write the converse,
  3. tell whether the converse is true or false.

Two angles are supplementary if the sum of their measures is 180.

Short Answer

Expert verified
  1. Given statement is true
  2. If two angles are supplementary then sum of their measure is180掳
  3. Converse statement is true.

Step by step solution

01

Part a. Step 1. Meaning of an angle.

An angle is a figure formed by two rays that share a common vertex.

02

Part a. Step 2. Meaning of given statement.

Consider the following figure:

鈭�1,鈭�2lie on a straight line,鈭�1+鈭�2=180

So, 鈭�1,鈭�2are said to be supplementary angles.

03

Part a. Step 3. Conclusion.

From first and second statement given statement is true.

04

Part b. Step 1. Converse of a statement.

Converse of a statement 鈥渋f P then Q鈥� is 鈥渋f Q then P鈥�

05

Part b.  Step 2. Find P and Q in given statement.

Pis 鈥渟um of measure of two angles is 180掳鈥�

Qis 鈥渢wo angles are supplementary鈥�

06

Part b. Step 3. Converse of given statement.

If two angles are supplementary then sum of their measure is180掳

07

Part c. Step 1. Meaning of supplementary angles.

Two angles are known as supplementary if their sum is180掳

08

Part c. Step 2. Meaning of converse statement.

It is same as meaning of supplementary angles

09

Part c. Step 3. Conclusion.

Converse statement is true.

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