In triangle EFG the measure of angle E is four times the measure if angle F. The measure of angle G is 18 degrees less than the measure of angle E. What is the measure of each angle?

Question

Aedan Massey

Mathematics

23 July, 12:37

In triangle EFG the measure of angle E is four times the measure if angle F. The measure of angle G is 18 degrees less than the measure of angle E. What is the measure of each angle?

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Answers (1)

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Puck · Answer 1

Step-by-step explanation:

In our triangle, angles E + F + G = 180 degrees. If angle E is 4 times the measure of F, and G is 18 less than E, then

F is x,

E is 4x, and

G is 4x - 18

Add these all together and set the sum equal to 180:

x + 4x + 4x - 18 = 180

Combining like terms:

9x - 18 = 180 and

9x = 196 so

x = 22

That means that

F = 22,

E = 4 (22) = 88 and

G = 4 (22) - 18 = 88 - 18 = 70

Since 22 + 88 + 70 do in fact equal 180 you can be fairly certain that your answer is correct! (It is correct ... trust me!)