Question

The folding chair has different settings that change the angles formed by its parts. Suppose angle 2 is 31 and angle 3 is 72. Find the measure of angle 1.

Answer 1

103°

Explanation:

Consider triangle with angles 2, 3 and supplementary angele to angle 1.

In this triangle, angles 2 and 3 are interior angles, angle 1 is exterior angle opposit to two given interior angles.

Exterior Angle Theorem: The exterior angle of the triangle is equal to the sum of the two opposite interior angles.

Since

`m\angle 2=31^(\circ)\\ \\m\angle 3=72^(\circ),`

by exterior angle theorem

`m\angle 1=m\angle 2+m\angle 3\\ \\m\angle 1=31^(\circ)+72^(\circ)\\ \\m\angle 1=103^(\circ)`