Question

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

Explanation:

Step1: Recall isosceles - triangle property

In an isosceles triangle, base - angles are equal. So, $\angle B=\angle G=(x + 10)^{\circ}$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, $(x + 10)+(x + 10)+3x=180$.

Step3: Simplify the equation

Combine like terms: $x+x + 3x+10 + 10=180$, which gives $5x+20 = 180$.

Step4: Solve for $x$

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

Step5: Find the measure of $\angle B$

Substitute $x = 32$ into the expression for $\angle B$. $\angle B=(x + 10)^{\circ}=(32+10)^{\circ}=42^{\circ}$.

Answer:

$42^{\circ}$