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Answer:
2-Given that y : z = 3 : 7
Let ∠ y = 3a
Then ∠z = 7a
∠x and ∠z are alternate interior angles of parallel lines so that
∠x = ∠z …(1)
Sum of interior angle on the same side of the transversal is always = 180°
So that
x + y = 180°
plug the value of x from equation (1)
z + y = 180°
plug the value of z and y we get
7a + 3a = 180°
10 a = 180°
a = 180°/10
a = 18
y = 3a = 3x18 = 54°
z = 7a = 7x18 = 126°
x = z = 126°
3-∠GEF + ∠FEG = ∠GED
EF ⊥ CD so that ∠ FED = 90°
And given that ∠ GED = 126°
∠GEF + 90° = 126°
∠GEF = 126°- 90°
∠GEF = 36°
AB || CD, EF ⊥ CD so ∠EFG = 90°
Use angle sum property of triangle (sum is 180°)
∠GEF + ∠EFG + ∠FGE = 180°
Plug the values we get
36° + 90° + ∠FGE = 180°
∠FGE = 180° – 36° - 90°
∠FGE = 54°
AB is a straight line so that use linear pair property
∠AGE +∠FGE = 180°
Plug the value of ∠FGE = 54°
We get
∠AGE +54° = 180°
∠AGE = 180° - 54°
∠AGE = 126°
angle age -126 ; angle gef 36 ; fge -54
