Question

For triangle EFG shown below, what is the measure of the exterior angle at vertex G?

E
(1) 27°
(3) 74°
47°
(2) 47°
(4) 94°
27°
106°
G
F

Answer 1

The measure of the exterior angle at vertex G in triangle EFG is (4) 94°.

Step-by-step explanation:

In a triangle, the sum of the measures of the interior angles is always 180°. The exterior angle at any vertex of a triangle is equal to the sum of the measures of its two non-adjacent interior angles. For triangle EFG, the exterior angle at vertex G is formed by angles E and F.

Let's denote the measures of angles E, F, and the exterior angle at G as θE, θF, and θG, respectively. According to the exterior angle theorem:

`\[ θG = θE + θF \]`

The given answer choices are 27°, 47°, 74°, and 94°. To find the correct answer, we need to consider the options. Since the exterior angle is formed by the sum of angles E and F, the answer must be greater than the largest of the interior angles, which is 74°. Therefore, the only suitable option is (4) 94°.

In conclusion, the measure of the exterior angle at vertex G is 94°, as it is the sum of angles E and F. This answer aligns with the principles of the exterior angle theorem and the properties of triangles.

Answer 2

Can u show the triangle ?