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Q9.

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 $\angle A,\text{and}\angle D$.