Question

(Name one pair of complementary angles and two pairs of supplementary angles) The points R, W and T are collinear, which two angles are complementary and which two angles are supplementary?

Answer 1

Explanation

Step 1

complementary angles =two angles whose sum is 90°.

then, search for two angles which sum is equal to 90 degrees, a right angle

$\begin{gathered} \text{PWQ} \\ \text{QWT} \end{gathered}$

because

$\begin{gathered} \text{PWQ}+\text{QWT}=\text{PWT} \\ \text{and PWT=90 degrees} \end{gathered}$

Step 2

supplementary angles

Two angles are supplementary when they add up to 180 degrees.

the angle RWT= 180

then we need to find two angle , wich that

angle 1 +angle 2 = RWT

it can be

$\begin{gathered} \text{RWP} \\ \text{and} \\ \text{PWT} \end{gathered}$

or

$\begin{gathered} \text{RWQ} \\ \text{and} \\ \text{QWT} \end{gathered}$

Step 3

The points R, W and T are collinear,it means all of then are over the same line

$\begin{gathered} \text{complementary} \\ \\ P\text{WQ and QWT} \\ \text{because} \\ P\text{WQ}+\text{QWT}=90 \end{gathered}$

Now, supplementary

$\begin{gathered} \text{supplementary} \\ \text{RWQ and QWT} \\ \text{because} \\ \text{RWQ + QWT}=180 \end{gathered}$