Chapter 12.1, Problem 9E

To determine

To Identify: The pair(s) of complementary angles in a quadrilateral.

Answer to Problem 9E

In the quadrilateral, $\angle A$ and $\angle D$ form a complementary angle pair.

Explanation of Solution

Given Information: A quadrilateral with its four angles having measures $\angle A={40}^o,\angle B={130}^o,\angle C={140}^o,\angle D={50}^o$ as shown below

  

Concept Used:If the sum of measures of two angles is ${90}^o$ then the angles are called complementary angles and if the sum is ${180}^o$ then the angles are called supplementary angles.

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

  $\angle A+\angle B={170}^o$

  $\angle A+\angle C={180}^o$

  $\angle A+\angle D={90}^o$

  $\angle B+\angle C={270}^o$

  $\angle B+\angle D={180}^o$

  $\angle C+\angle D={190}^o$

In the above list, only the pair ( $\angle A,\angle D$ ) have the sum of their measures equal to ${90}^o$ .

Therefore, the pair(s) of complementary angles in the quadrilateral is(are): ( $\angle A,\angle D$).