Question

Use the diagram shown. Identify all pairs of the specified angles.

Supplementary angles

Short answer

In the quadrilateral, $\angle A,\angle C$and$\angle B,\angle D$ form two supplementary angle pairs.

Step-by-step solution

Step 1. Given Information.

The figure is shown below.

Step 2. Concept used.

If the sum of two angles is $90°$ then the angles are called complementary angles and if the sum is $180°$ then the angles are called supplementary angles.

Step 3. Calculation.

The sum of measures of all the possible pairs of angles in the quadrilateral is,

$\begin{array}{c}\angle A+\angle B=170°\\ \angle A+\angle C=180°\\ \angle A+\angle D=90°\\ \angle B+\angle C=270°\end{array}$

And,

$\begin{array}{c}\angle B+\angle D=180°\\ \angle C+\angle D=190°\end{array}$

In the above list, only the pairs $\angle A,\angle C$ and $\angle B,\angle D$have the sum of their measures equal to $180°$.

Step 4. Conclusion.

The pairs of supplementary angles in the quadrilateral are $\angle A,\angle C$ and $\angle B,\angle D$.