Angle addition Postulate

Question

if m<EFH = (5x+1) , m< HFG = 62, and m< EFG = ( 18x-11),find each measure

Answer 1

If your sketch looks like this:

Then (by virtue of the angle addition postulate) we can say:

m∠EFH + m∠HFG = m∠EFG

substituting the vales of each angle we get:

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

5x + 1 + 62 = 18x - 11

5x + 63 = 18x - 11

63 = 13x - 11

74 = 13x

x = 74/13 (approx 5.692)

Plugging this value of "x" into the expressions:

m∠EFH = 5(74/13) + 1 = (383/13)° which is approx 29.5°

m∠HFG = 62°

m∠EFG = 18(74/13) - 11 = (1189/13)° which is approx 91.5°