Angle efg and angle gfh are a linear pair, the measure of angle efg equals 4n+20, and measure of angle gfh equals 3n+13. what are the measures of angle efg and angle gfh?

∠EFG=104° and ∠GFH=76°

Step-by-step explanation:

Given information:∠EFG = (4n+20)°, ∠GFH = (3n+13)° and ∠EFG and ∠GFH are a linear pair.

If two angles are a linear pair, then the sum of those angles is 180°.

It is given that ∠EFG and ∠GFH are a linear pair.

Substitute the given values.

Combined like terms.

Subtract 33 from both sides.

Divide both sides by 7.

The value of n is 21.

Therefore, the measure of ∠EFG and ∠GFH are 104° and 76° respectively.

1. 180°. the sum of the interior angles of a triangle is 180°, for the equilateral triangle that it has three equals side is 60°+60°+60°=180°.

2. 60°. each interior angle of a equilateral triangle is 60°

3. 120°. the measure of ∠m is 120°, the sum of the angles ∠m and ∠n is equal to 180°. so, in order to find the measure of ∠m, we have ∠m+∠n=180° > ∠m=180°-∠n > ∠m=180°-60°=120°.

4. 360°. the sum of the exterior angles of an equilateral triangle is ∠m+∠r+∠x=120°+120°+120°=360°. the exterior angles of any triangle always add 360°.