Question

1. part a use the figure above to determine the value of angle x° a. 62° b. 40° c. 75° d. 45° part b what is the value of y?

Explanation:

Step1: Use the exterior - angle theorem

The exterior - angle theorem states that an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. For the given triangle, \(x\) is an exterior angle. So, \(x = 43^{\circ}+75^{\circ}\).

$$x=43 + 75$$

$$x = 118^{\circ}$$

Wait, there is a mistake. Maybe it's the vertical - angle and the sum of angles in a triangle. The sum of angles in a triangle is \(180^{\circ}\). Let's first find the third angle of the triangle. Let the third angle of the triangle be \(z\). Then \(z=180-(43 + 75)=180 - 118=62^{\circ}\). Since \(x\) and \(z\) are vertical angles (opposite angles formed by the intersection of two lines), \(x = z\).

Step2: Determine the value of \(y\)

Since \(x\) and \(y\) are supplementary angles (they form a linear pair, and the sum of angles on a straight line is \(180^{\circ}\)), if \(x = 62^{\circ}\), then \(y=180 - x\).

$$y=180-62$$

$$y = 118^{\circ}$$

Answer:

Part A: A. \(62^{\circ}\)
Part B: \(118^{\circ}\)