Question

triangle qrs is a right triangle with the right angle at vertex r. the sum of m∠q and m∠s must be equal to 45°. greater than 45° and less than 90°. equal to 90°. greater than 90° and less than 180°.

Explanation:

Step1: Recall the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). For \(\triangle QRS\), we have \(m\angle Q + m\angle R+ m\angle S=180^{\circ}\).

Step2: Substitute the value of \(m\angle R\)

Since \(\angle R\) is a right angle, \(m\angle R = 90^{\circ}\). Substituting into the equation \(m\angle Q + m\angle R+ m\angle S=180^{\circ}\), we get \(m\angle Q+90^{\circ}+m\angle S = 180^{\circ}\).

Step3: Solve for \(m\angle Q + m\angle S\)

Subtract \(90^{\circ}\) from both sides of the equation \(m\angle Q+90^{\circ}+m\angle S = 180^{\circ}\).

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Answer:

equal to \(90^{\circ}\)