Question

use the diagram below to answer the questions on the right:
create a triangle angle sum equation to solve for:
(a) 2x + 50 + 2x = 180
(b) solve for x:
32.5
(c) what is the measure of both ∠a and ∠c?
65

Explanation:

Step1: Recall angle - sum property

The sum of interior angles of a triangle is 180°. In triangle ABC, we have ∠A + ∠B+∠C = 180°. Given ∠B = 50°, ∠A=2x and ∠C = 2x, the equation is 2x + 50+2x=180.

Step2: Solve the equation for x

Combine like - terms: 4x+50 = 180. Subtract 50 from both sides: 4x=180 - 50=130. Then divide both sides by 4: $x=\frac{130}{4}=32.5$.

Step3: Find the measure of ∠A and ∠C

Since ∠A = ∠C = 2x, substitute x = 32.5 into 2x. So 2x=2×32.5 = 65.

Answer:

(a) 2x + 50+2x = 180
(b) 32.5
(c) 65