Question

what is the degree measure of x? a 67° b 88° c 111° d 134°

Explanation:

Step1: Find the third angle of the triangle

The sum of the interior angles of a triangle is \(180^\circ\). Given two angles are \(46^\circ\) and \(88^\circ\), the third angle \(y\) is calculated as:
\(y = 180^\circ - 46^\circ - 88^\circ = 46^\circ\)? Wait, no, wait, let's recalculate. Wait, the triangle has angles \(46^\circ\), \(88^\circ\), so the third angle (let's call it \(z\)): \(z = 180 - 46 - 88 = 46\)? Wait, no, maybe I misread the triangle. Wait, the triangle has one angle \(46^\circ\), another \(88^\circ\), so the third angle adjacent to the exterior angle \(x\) is supplementary to \(x\). Wait, the exterior angle theorem: the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step2: Apply the exterior angle theorem

The exterior angle \(x\) is equal to the sum of the two non - adjacent interior angles of the triangle. The two non - adjacent interior angles are \(46^\circ\) and \(88^\circ\). So, \(x=46^\circ + 88^\circ=134^\circ\)? Wait, no, wait, let's check again. Wait, maybe the triangle angles are \(46^\circ\), \(88^\circ\), so the third angle (let's say angle at the vertex opposite to the side with the exterior angle) is \(180-(46 + 88)=46^\circ\). Then the exterior angle \(x\) and this third angle are supplementary? No, the exterior angle is equal to the sum of the two remote interior angles. Wait, the two remote interior angles from the exterior angle \(x\) are \(46^\circ\) and \(88^\circ\). So \(x = 46+88 = 134^\circ\). Wait, but let's check the options. Option D is \(134^\circ\). Wait, maybe I made a mistake in the first step. Let's recalculate the sum of the two non - adjacent angles: \(46 + 88=134\). So the exterior angle \(x\) is equal to the sum of the two non - adjacent interior angles. So \(x = 46+88 = 134^\circ\).

Answer:

D. \(134^\circ\)