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Q9.

Expert-verifiedFound in: Page 689

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.

The figure is shown below.

If the **sum of two angles is $90\xb0$ then the angles are called complementary** angles and **if the sum is $180\xb0$ then the angles are called supplementary angles**.

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

$\begin{array}{c}\angle A+\angle B=170\xb0\\ \angle A+\angle C=180\xb0\\ \angle A+\angle D=90\xb0\\ \angle B+\angle C=270\xb0\end{array}$

And,

$\begin{array}{c}\angle B+\angle D=180\xb0\\ \angle C+\angle D=190\xb0\end{array}$

In the above list, only the pair $\angle A,\text{and}\angle D$ have the sum of their measures equal to $90\xb0$.

The pair of complementary angles in the quadrilateral is $\angle A,\text{and}\angle D$.

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