# In Fig. 6.30, if AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE.

**Solution:**

Given: AB || CD, EF ⊥ CD and ∠GED =126°

To Find: ∠AGE, ∠GEF and ∠FGE

When two lines intersect, the sum of adjacent angles is supplementary.

When two parallel lines are cut by a transversal, alternate interior angles formed are equal.

Let ∠AGE = x, ∠GEF = y and ∠FGE = z.

From the figure, we can see that,

∠GED = ∠GEF + ∠FED

∠GEF = ∠GED - ∠FED

y = 126° - 90° [ Since, ∠GED = 126° and ∠FED = 90°]

y = 36°

Thus, ∠GEF = y = 36°

AB and CD are parallel lines cut by a transversal, thus the pair of alternate interior angles formed are equal.

∠AGE = ∠GED

Thus, ∠AGE = x = 126°

Line AB is intersected by line GE where x and z forms a linear pair.

x + z = 180°

126° + z = 180°

z = 180° - 126° = 54°

Thus, ∠FGE = z = 54°

**☛ Check: **NCERT Solutions Class 9 Maths Chapter 6

**Video Solution:**

## In Fig. 6.30, if AB || CD, EF ⊥ CD and ∠GED =126°, find ∠AGE, ∠GEF and ∠FGE.

NCERT Solutions Class 9 Maths Chapter 6 Exercise 6.2 Question 3

**Summary:**

In Fig. 6.30, if AB || CD, EF⊥CD, and ∠GED = 126°, then the values of ∠AGE, ∠GEF, and ∠FGE are 126°, 36°, and 54° respectively.

**☛ Related Questions:**

- In Fig. 6.28, find the values of x and y and then show that AB||CD.
- In Fig. 6.29, if AB || CD, CD || EF and y : z = 3 : 7, find x.
- In Fig. 6.31, if PQ || ST, ∠PQR = 110° and ∠RST = 130°, find ∠QRS.[Hint: Draw a line parallel to ST through point R.]
- In Fig. 6.32, if AB || CD, ∠APQ = 50° and ∠PRD = 127°, find x and y.