Question

suppose △ bug is an isosceles triangle. find the measure of ∠ b.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In an isosceles triangle △BUG, ∠B=(x + 10)°, ∠U = (3x)°, and ∠G=∠B=(x + 10)° (since the base - angles of an isosceles triangle are equal). So, (x + 10)+(3x)+(x + 10)=180.

Step2: Simplify the equation

Combine like - terms: 5x+20 = 180.

Step3: Solve for x

Subtract 20 from both sides: 5x=180 - 20=160. Then divide both sides by 5: x = $\frac{160}{5}$=32.

Step4: Find the measure of ∠B

Substitute x = 32 into the expression for ∠B. ∠B=(x + 10)°. So, ∠B=(32 + 10)°=42°.

Answer:

42°