Page 4 - Ans Sub

3x – 20 = 2x + 10
We know that the two lines are parallel if the corresponding angles are equal
3x – 2x = 10 + 20
On further calculation
x = 30
0
Therefore, the value of x is 30 .
5. In figure, if AB || CD, EF ⊥ CD and ∠GED = 126°, find ∠AGE, ∠GEF and ∠FGE.

Solution:
AB || CD and GE is a transversal.
∴∠AGE = ∠GED [Alternate interior angles]
But ∠GED = 126° [Given]
∴∠AGE = 126°
Also, ∠GEF + ∠FED = ∠GED
or ∠GEF + 90° = 126° [∵ EF ⊥ CD (given)]
x = z [Alternate interior angles]… (1) Again, AB || CD
⇒ x + y = 180° [Co-interior angles]
∠GEF = 126° -90° = 36°
Now, AB || CD and GE is a transversal.
∴∠FGE + ∠GED = 180° [Co-interior angles]
or ∠FGE + 126° = 180°
or ∠FGE = 180° – 126° = 54°
Thus, ∠AGE = 126°, ∠GEF=36° and ∠FGE = 54°.
6.
In the given figure, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°,
then find ∠QRS.

Solution:
Given: AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°
To find: ∠QRS

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