Question

In AABC, m/B = 44x and m/C= 8x. Write and solve an
equation to find the measure of each angle.

Answer 1

• m∠A = 24°
• m∠B = 132°
• m∠C = 24

Explanation:

ΔABC is an isosceles triangle, which is indicated by the marks on the two sides.

Isosceles triangles are triangles that have two equal side lengths and angles. So here, ∠A and ∠C have the same angle measures.

Additionally, the sum of the three angles of any triangle sums up to 180°.

..................................................................................................................................................

Given: m∠A = 8x, m∠B = 44x, and m∠C = 8x

Step 1: Set the measure of the angles to equal 180.

`\implies 8x+44x+8x=180`

`\implies 60x=180`

Step 2: Divide both sides by 60.

`\implies (60x)/(60)=(180)/(60)`

`\implies x=3`

Step 3: To find the measure of each angle, substitute 3 for x.

`\implies m \angle A = 8(3) = 24^\circ`

`\implies m \angle B = 44(3) = 132^\circ`

`\implies m \angle C = 8(3) = 24^\circ`

The measures of ∠A, ∠B, and ∠C all sum up to 180°.