Question

the measure of \angle gur can be calculated. m\angle gur = \square

Explanation:

Step1: Find the measure of the adjacent angle to \(160^{\circ}\)

Since \(XUH\) is a straight line (\(180^{\circ}\)), the adjacent angle to \(160^{\circ}\) is \(180 - 160=20^{\circ}\).

Step2: Calculate \(m\angle GUR\)

We know that one of the angles in the right - angled part (where there is a right angle, \(90^{\circ}\)) and we have a \(20^{\circ}\) angle. Using the relationship in the angles formed (\(m\angle GUR+20^{\circ}+90^{\circ}=180^{\circ}-20^{\circ}\) (the other \(20^{\circ}\) from step 1 is part of the non - right - angled part of the angle composition). More simply, \(m\angle GUR=90 - 20 - 20\).

$$m\angle GUR=50^{\circ}$$

Answer:

\(50\)