Question

solve for x. round to the nearest tenth of a degree, if necessary.
answer attempt 1 out of a
x =

Explanation:

Step1: Identify the type of triangle

Since \(OP = OQ = 8.7\) and \(\angle P=90^{\circ}\), \(\triangle OPQ\) is an isosceles right - triangle. In an isosceles right - triangle, the two non - right angles are equal.

Step2: Use the angle - sum property of a triangle

The sum of angles in a triangle is \(180^{\circ}\). Let \(x\) be the measure of \(\angle O\). We know that \(\angle P = 90^{\circ}\), and \(\angle O=\angle Q=x\) (because \(OP = OQ\)). Then, using the formula \(\angle O+\angle Q+\angle P=180^{\circ}\), we substitute the values: \(x + x+90^{\circ}=180^{\circ}\).

Step3: Solve the equation for \(x\)

Combine like terms: \(2x=180^{\circ}-90^{\circ}\). So, \(2x = 90^{\circ}\). Divide both sides by 2: \(x=\frac{90^{\circ}}{2}\).

Answer:

\(45\)