Question

If EFH = (5x + 1)°, HFG = 62°, and EFG = (18x + 11)°, find EFH

Answer 1

Given:

Consider the below figure attached with this question.

∠EFH = (5x + 1)°, ∠HFG = 62°, and ∠EFG = (18x + 11)°

To find:

The measure of ∠EFH.

Solution:

From the figure it is clear that ∠EFG is divide in two parts ∠EFH and ∠HFG. So,

$\angle EFG=\angle EFH+\angle HFG$

$18x+11=(5x+1)+(62)$

$18x+11=5x+63$

Isolate variable terms.

$18x-5x=63-11$

$13x=52$

Divide both sides by 13.

$x=\dfrac{52}{13}$

$x=4$

The value of x is 4.

$\angle EFH=(5x+1)^\circ$

$\angle EFH=(5(4)+1)^\circ$

$\angle EFH=(20+1)^\circ$

$\angle EFH=21^\circ$

Therefore, the measure of ∠EFH is 21°.