Question

what is the measure of angle b in this triangle?
enter your answer in the box.

m∠b=□°

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(40+(2x - 30)+(x + 20)=180\).
Simplify the left - hand side: \(40+2x-30+x + 20=180\), which becomes \(3x + 30=180\).

Step2: Solve for \(x\)

Subtract \(30\) from both sides: \(3x=180 - 30\), so \(3x=150\).
Divide both sides by \(3\): \(x=\frac{150}{3}=50\).

Step3: Find the measure of angle \(B\)

Since \(m\angle B=(2x - 30)^{\circ}\), substitute \(x = 50\) into the expression.
\(m\angle B=2\times50-30\).
\(m\angle B=100 - 30\).

Answer:

\(70\)