Question

vertical/adjacent/complementary angles
question
solve for the value of q.
answer
attempt 1 out of 2
q = submit answer

Explanation:

Step1: Recall the sum of angles around a right - angle

The sum of the three angles is \(180^{\circ}\). One angle is \(90^{\circ}\), another is \(57^{\circ}\), and the third is \((8q + 1)^{\circ}\). So, \(57+(8q + 1)+90=180\).

Step2: Simplify the left - hand side of the equation

First, combine like terms: \(57+90 + 1+8q=180\), which gives \(148+8q=180\).

Step3: Solve for \(q\)

Subtract \(148\) from both sides: \(8q=180 - 148\), so \(8q=32\). Then divide both sides by \(8\): \(q=\frac{32}{8}\).

Answer:

\(q = 4\)