Chapter 12.1, Problem 10E

To determine

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

Answer to Problem 10E

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

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 pairs $\angle A,\angle C$ and $\angle B,\angle D$ have the sum of their measures equal to ${180}^o$ .

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