Question

3 multiple choice 25 points find the value of x. encuentra el valor de x. triangle with angles 86°, 33°, y°, and exterior angle x° options: 86°, 119°, 61°, 33°

Explanation:

Step1: Find y using triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(33^\circ + 86^\circ + y^\circ = 180^\circ\).
Calculating: \(y = 180 - 33 - 86 = 61^\circ\).

Step2: Find x using linear pair

\(x\) and \(y\) form a linear pair (supplementary angles), so \(x + y = 180^\circ\).
Substituting \(y = 61^\circ\): \(x = 180 - 61 = 119^\circ\). Wait, no—wait, correction: Wait, actually, the exterior angle theorem: the exterior angle \(x\) is equal to the sum of the two non - adjacent interior angles. So \(x = 33^\circ+86^\circ = 119^\circ\)? Wait, no, wait the triangle angles: 33, 86, so y is 180 - 33 - 86 = 61. Then x and y are supplementary, so x = 180 - 61 = 119? Wait, but let's check again. Wait, the triangle has angles 33, 86, and y. So 33 + 86 + y = 180. 33+86 is 119, so y = 180 - 119 = 61. Then x and y are adjacent and form a straight line, so x + y = 180. So x = 180 - 61 = 119. Wait, but the options have 119 as an option. Wait, but let's check the exterior angle theorem: the exterior angle is equal to the sum of the two remote interior angles. So the two remote interior angles are 33 and 86, so x = 33 + 86 = 119. Yes, that's correct.

Answer:

119° (corresponding to the option with 119°)