Question

EFG and ∠GFH are a linear​ pair, m∠EFG=3n+25​, and m∠GFH=4n+36. What are m∠EFG and m∠​GFH? m∠EFG = nothing° m∠GFH = nothing

Answer 1

To find the measure of angles ∠EFG and ∠GFH that form a linear pair, we solve the equation set up by their supplementary relationship. We find that m∠EFG is 76° and m∠GFH is 104°.

Step-by-step explanation:

If ∠EFG and ∠GFH form a linear pair, then their measures should add up to 180° because linear pairs are supplementary. The problem provides us with the expressions for the measures of these angles, which are m∠EFG = 3n + 25 and m∠GFH = 4n + 36. To find the measure of each angle, we can set up an equation where the sum of m∠EFG and m∠GFH equals 180°.

(3n + 25) + (4n + 36) = 180
Simplify the equation: 7n + 61 = 180
Solve the equation for n: n = 17

Substitute n back into the expressions to find the measures of ∠EFG and ∠GFH:

• m∠EFG = 3(17) + 25 = 76°
• m∠GFH = 4(17) + 36 = 104°