Question

Geometry help needed!

In the figure below, what are the measures of ∠A and ∠B?

Answer 1

`\huge\boxed{\sf \angle A = 43\°}`

`\huge\boxed{\sf \angle B = 59\°}`

Explanation:

Finding Angle B:

• Interior angles of a triangle add up to 180 degrees.

In ΔDBC,

98 + ∠B + 31 = 180°

∠B + 121 = 180

∠B = 180 - 121

∠B = 59°

Finding Angle A:

• The measure of exterior angle is equal to the sum of non-adjacent interior angles.

So,

∠C (Exterior Angle) = ∠A + ∠B

102 = ∠A + 59

• Subtract 59 from both sides

102 - 59 = ∠A

43 = ∠A

∠A = 43°

`\rule[225]{225}{2}`