Question

1. the figure shows three exterior angles of △abc. show that m∠1 + m∠2 + m∠3 = 360°. 6. find the values of x and y.

Explanation:

Step1: Find the value of \(x\)

Use the property that vertical angles are equal and the sum of interior angles of a triangle is \(180^{\circ}\).
The vertical angle of \(85^{\circ}\) is \(85^{\circ}\). In the left - hand triangle, we have \(x + 68+85 = 180\).

$$x=180-(68 + 85)=180 - 153=27$$

Step2: Find the value of \(y\)

First, find the third interior angle of the right - hand triangle. The sum of interior angles of a triangle is \(180^{\circ}\). Let the third interior angle be \(z\), then \(z=180-(72 + 85)=180 - 157 = 23\).
Since \(y\) is an exterior angle of the right - hand triangle, and an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. Here, \(y = 72+23\) (using the exterior angle theorem).

$$y = 95$$

Answer:

\(x = 27\) and \(y = 95\)