Question

In each figure below, there are three angles. The measures of two are given alongside. Can you find the third?

A.

B.

C.

D.

Answer 1

(A) Given ∠BAC = 30° and ∠CAD = 40°

∠BAD = ∠BAC + ∠CAD

= 30° + 40°

= 70°

(B) Given ∠BAC = 60° and ∠CAD = 45°

∠BAD = ∠BAC + ∠CAD

= 60° + 45°

= 105°

(C) Given ∠BAC = 50° and ∠BAD = 90°

∠BAD = ∠BAC + ∠CAD

⇒ ∠CAD = ∠BAD − ∠BAC

= 90° − 50°

= 40°

(D) Given ∠CAD = 50° and ∠BAD = 100°

∠BAD = ∠BAC + ∠CAD

⇒ ∠BAC = ∠BAD − ∠CAD

= 100° − 50°

= 50°