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Expert-verified Found in: Page 689 ### Pre-algebra

Book edition Common Core Edition
Author(s) Ron Larson, Laurie Boswell, Timothy D. Kanold, Lee Stiff
Pages 183 pages
ISBN 9780547587776 # Use the diagram shown. Identify all pairs of the specified angles.Complementary angles In the quadrilateral, $\angle A$ and $\angle D$ form a complementary angle pair.

See the 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 pair $\angle A,\text{and}\angle D$ have the sum of their measures equal to $90°$.

## Step 4. Conclusion.

The pair of complementary angles in the quadrilateral is $\angle A,\text{and}\angle D$. ### Want to see more solutions like these? 