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Chapter 2: Q19. (page 71)

Classify each statement as true or false. If it is false, provide a counter example.

Ifm鈭�A=45掳, then the complement of鈭燗is one third of its supplement.

Short Answer

Expert verified

The statement is True.

Step by step solution

01

Step 1. State the definition of complementary and supplementary angles.

Two angles are said to be complementary if the sum of those two angles is90掳.

Two angles are said to be supplementary if the sum of those two angles is 180掳.

02

Step 2. Show the calculation.

First calculate the complement of 鈭燗.

As sum of two complementary angles is 90掳,

Then, complement of 鈭燗 is 90掳-45掳=45掳.

Now, calculate supplement of 鈭燗,

鈭�A=45掳

As sum of two supplementary angles is 180掳,

Then, supplement of 鈭燗 is 180掳-45掳=135掳.

Now check whether the statement 鈥淚f m鈭�A=45掳, then the complement of 鈭燗 is one third of its supplement鈥�.

Here,

Complementof鈭�A=45掳=13135掳=13Supplementof鈭�A

03

Step 3. State the conclusion.

Therefore, the statement True.

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