Question

What type of angle is ∠CEB ?

acute

right

obtuse

straight

Answer 1

BED and CEB are supplementary angles, meaning their sum is 180°. You already know BED is 77°, so you subtract 77° from 180° to find CEB.

180° - 77° = 103°

CEB = 103°

Because it is greater than 90°, it is obtuse.

Answer 2

∠CEB and ∠AED are vertical angles, which means they must be equal to each other. Make them = x in an equation. The angles form a quadrilateral, so the sum of the interior angles must equal 360°.

77 + 77 + x + x = 360
Combine like terms.

154 + 2x = 360
Subtract 154 from both sides.

2x = 206
Divide both sides by 2.

x = 103

∠CEB is greater than 90°, so it must be an obtuse angle.