Question

triangle qrs is a right triangle with the right angle at vertex r. the sum of ( mangle q ) and ( mangle s ) must be greater than ( 45^{circ} ) and less than ( 90^{circ} ). greater than ( 90^{circ} ) and less than ( 180^{circ} ). equal to ( 45^{circ} ). equal to ( 90^{circ} )

Explanation:

Step1: Recall the triangle angle - sum theorem

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

Step2: Substitute the measure of the right - angle

Since \(\angle R\) is a right - angle, \(m\angle R = 90^{\circ}\). Then \(m\angle Q + 90^{\circ}+ m\angle S=180^{\circ}\).

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

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

Answer:

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