Question

In each diagram line k is parallel to line l and line t intersects lines k and l.

Based on the diagram complete a true statement about x, by using the answer bank.

Answer 1

x = 7.5

m∠EGB = 75°

m∠EGA = 105°

Explanation:

According to the Alternate Exterior Angles Theorem, angles EGB and CHF are equivalent. This means we can find x by setting them equal to each other.

10x = 2x + 60 (subtract 2x from both sides)

8x = 60 (divide both sides by 8)

x = 7.5

We can now plug in x to find m∠EGB.

2(7.5) + 60 = 15 + 60 = 75

Therefore, m∠EGB = 75°

As EGB and EGA are supplementary angles, that means that together, they add up to 180°. That means:

75 + EGA = 180 (subtract 75 from both sides)

m∠EGA = 105°