Question

Find the measures of angle GCH and angle AGH​

Answer 1

Answer:

Angle GCH = 50°

Angle AGH = 100°

Step-by-step explanation:

If EF II BC and HC is transversal, then

Angle GCH = 50° (Alternate Interior Angles)

[First angle found]

Now, for Angle AGH,

Angle CHG = 50° (Vertically Opposite Angles)

And, we know that Angle HCB = 50°

Hence, in triangle CGH, By angle sum property,

Angle CHG + Angle HCG + Angle CGH = 180°

50 + 50 + Angle CGH = 180

Angle CGH = 180 – 100

= 80°

Now,

Angle CGH + Angle AGH = 180° (Linear Pair)

80° + Angle AGH = 180

Angle AGH = 180 - 80

= 100°

[Angle AGH found]

There is one more way to find Angle AGH.

We know that Angle GCH = Angle CHG = 50°

Then in triangle CGH, by exterior angle property,

Angle AGH = Angle GCH + Angle CHG

= 50 + 50

= 100°

Hence, proved.

(hope it helped ☺️)