Lines and Angles

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

n the given figure, the arms of two angles are parallel.

If ∠ ABC = 70°, then find

(i) ∠ DGC

(ii) ∠ DEF

Find the value of x in each of the following figures if l || m.

In the adjoining figure, p || q. Find the unknown angles.

In the adjoining figure, identify

(i) The pairs of corresponding angles

(ii) The pairs of alternate interior angles

(iii) The pairs of interior angles on the same side of the transversal

(iv) The vertically opposite angles

State the property that is used in each of the following statements?

(i) If a||b, then ∠ 1 = ∠ 5

(ii) If ∠ 4 = ∠ 6, then a||b

(iii) If ∠ 4 + ∠ 5 = 180°, then a||b

In the adjoining figure, name the following pairs of angles.

(i) Obtuse vertically opposite angles

(ii) Adjacent complementary angles

(iii) Equal supplementary angles

(iv) Unequal supplementary angles

(v) Adjacent angles that do not form a linear pair

Fill in the blanks:

(i) If two angles are complementary, then the sum of their measures is _______.

(ii) If two angles are supplementary, then the sum of their measures is _______.

(iii) Two angles forming a linear pair are _______.

(iv) If two adjacent angles are supplementary, they form a _______.

(v) If two lines intersect at a point, then the vertically opposite angles are always _______.

(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are _______.

Find the value of the angles x, y, and z in each of the following:

In the following figure, is ∠ 1 adjacent to ∠ 2? Give reasons.

Indicate which pairs of angles are:

(i) Vertically opposite angles. (ii) Linear pairs.

Can two angles be supplementary if both of them are:

(i) Acute? (ii) Obtuse? (iii) Right?

An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45°?

In the adjoining figure:

(i) Is ∠ 1 adjacent to ∠ 2?

(ii) Is ∠ AOC adjacent to ∠ AOE?

(iii) Do ∠ COE and ∠ EOD form a linear pair?

(iv) Are ∠ BOD and ∠ DOA supplementary?

(v) Is ∠ 1 vertically opposite to ∠ 4?

(vi) What is the vertically opposite angle of ∠ 5?

In the given figure, ∠ 1 and ∠ 2 are supplementary angles. If ∠ 1 is decreased, what changes should take place in ∠ 2 so that both the angles still remain supplementary.

Find the angle which is equal to its supplement.

Find the angle which is equal to its complement.

Identify which of the following pairs of angles are complementary and which are supplementary.

(i) 65°, 115° (ii) 63°, 27°

(iii) 112°, 68° (iv) 130°, 50°

(v) 45°, 45° (vi) 80°, 10°

Find the supplement of each of the following angles:

Find the complement of each of the following angles: