**Lines and Angles**

**Question 1.****State the property that is used in each of the following statements?**

**Solution:**

**(i)**Corresponding angle property.

**(ii)**Alternate interior angle property.

**(iii)**Interior angles on the same side of the transversal are supplementary.

**Question 2.****In the adjoining figure, identify :**

- the pairs of corresponding angles.
- the pairs of alternate interior angles.
- the pairs of interior angles on the same side of the transversal.
- the vertically opposite angles

**Solution:**

- ∠1, ∠5; ∠2, ∠6; ∠3, ∠7 and ∠4, ∠8 are four pairs of corresponding angles.
- ∠2, ∠8 and ∠3, ∠5 are two pairs of alternate interior angles.
- ∠2, ∠5 and ∠3, ∠8 are two pairs of interior angles on the same side of the transversal.
- ∠1, ∠3; ∠2, ∠4; ∠5, ∠7 and ∠6, ∠8 are four pairs of vertically opposite angles.

**Question 3.****In the adjoining figure p || q. Find the unknown angles**

**Solution:**

**Question 4.****Find the value of x in each of the following figures if l || m :**

**Solution:**

**(i)**Since, l || m and t is a transversal.

∴ ∠x = (180° – 110°) = 70° [Corresponding angles, Linear pair]

**(ii)** if l || m and a is a transversal.

Then, ∠x = 1000 [Corresponding angles]

**Question 5.****In the given figure, the arms of two angles are parallel. If ∠ABC = 70°, then find**

**(i)**DGC

**(ii)**DEF

**Solution:**

**Question 6.****In the given figures below, decide whether l is parallel to m.**

**Solution:**