Question

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

If$m\angle A=45°$, then the complement of∠Ais one third of its supplement.

Short answer

The statement is True.

Step-by-step solution

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°.

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

Step 2. Show the calculation.

First calculate the complement of ∠A.

As sum of two complementary angles is 90°,

Then, complement of ∠A is $90°-45°=45°$.

Now, calculate supplement of ∠A,

$\angle A=45°$

As sum of two supplementary angles is 180°,

Then, supplement of ∠A is $180°-45°=135°$.

Now check whether the statement “If $m\angle A=45°$, then the complement of ∠A is one third of its supplement”.

Here,

$\text{Complementof}\angle A=45°=\frac{1}{3}\left(135°\right)=\frac{1}{3}\left(\text{Supplementof}\angle A\right)$

Step 3. State the conclusion.

Therefore, the statement True.