Question

solve for the value of q.

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \((2q - 3)+(5q + 2)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(2q-3 + 5q+2=(2q + 5q)+(-3 + 2)=7q-1\). The equation becomes \(7q-1 = 90\).

Step3: Solve for \(q\)

Add \(1\) to both sides: \(7q-1+1=90 + 1\), which gives \(7q=91\). Then divide both sides by \(7\): \(q=\frac{91}{7}\).

Answer:

\(q = 13\)