Question

question 46 of 50
using the figure below, determine the value of x.
triangle with angles 50° and 65°, and an exterior angle x°
options:
115?
50?
65?
15?
none of the choices are correct.

Explanation:

Step1: Find the third angle of the triangle

The sum of angles in a triangle is \(180^\circ\). So the third angle (let's call it \(y\)) is \(180 - 50 - 65 = 65^\circ\)? Wait, no, wait. Wait, the angle adjacent to \(x\) and the third angle of the triangle are supplementary? Wait, no, the exterior angle theorem: the exterior angle \(x\) is equal to the sum of the two non - adjacent interior angles. So the two non - adjacent interior angles are \(50^\circ\) and \(65^\circ\). So \(x=50 + 65=115^\circ\).
Wait, let's do it step by step. First, in a triangle, the sum of interior angles is \(180^\circ\). Let the angle adjacent to \(x\) (the one inside the triangle) be \(z\). Then \(50+65 + z=180\). So \(z = 180-(50 + 65)=180 - 115 = 65^\circ\). Then, since \(z\) and \(x\) are supplementary (they form a linear pair), \(x+z = 180\). So \(x=180 - z=180 - 65 = 115^\circ\).

Step2: Match with the options

We calculated \(x = 115^\circ\), and one of the options is \(115^\circ\) (the first option, although there is a typo with the question mark, but it's \(115\)).

Answer:

115 (the option with 115, assuming the typo is a mistake and it's \(115^\circ\))