Question

question 1 (multiple choice worth 2 points)
(polygon angle sums mc)

triangle abc has the following angle measures:

m∠a=(x + 4)°, m∠b=(2x - 11)°, m∠c=(3x + 25)°

what is m∠b?

27°

33°

43°

55°

Explanation:

Step1: Use triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \((x + 4)+(2x-11)+(3x + 25)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \((x+2x + 3x)+(4-11 + 25)=180\), which is \(6x+18 = 180\).

Step3: Solve for \(x\)

Subtract 18 from both sides: \(6x=180 - 18\), so \(6x=162\). Then divide both sides by 6: \(x=\frac{162}{6}=27\).

Step4: Find \(m\angle B\)

Substitute \(x = 27\) into the expression for \(m\angle B\). Since \(m\angle B=(2x-11)^{\circ}\), then \(m\angle B=(2\times27-11)^{\circ}=(54 - 11)^{\circ}=43^{\circ}\).

Answer:

\(43^{\circ}\)