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

Answer:

103°

Step-by-step 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

$m\angle 1=m\angle 2+m\angle 3\\ \\m\angle 1=31^{\circ}+72^{\circ}\\ \\m\angle 1=103^{\circ}$