In Fig. 6.1, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is

An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is

The angles of a triangle are in the ratio 5: 3: 7. The triangle is

If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be

In Fig. 6.2, POQ is a line. The value of x is

In Fig. 6.3, if OP||RS, ∠OPQ = 110° and ∠QRS = 130°, then ∠PQR is equal to

Angles of a triangle are in the ratio 2: 4: 3. The smallest angle of the triangle is

For what value of x + y in Fig. 6.4 will ABC be a line? Justify your answer.

Can a triangle have all angles less than 60°? Give reason for your answer.

Can a triangle have two obtuse angles? Give reason for your answer.

How many triangles can be drawn having its angles as 45°, 64° and 72°? Give reason for your answer.

How many triangles can be drawn having its angles as 53°, 64° and 63°? Give reason for your answer.

In Fig. 6.5, find the value of x for which the lines l and m are parallel.

Two adjacent angles are equal. Is it necessary that each of these angles will be a right angle? Justify your answer.

If one of the angles formed by two intersecting lines is a right angle, what can you say about the other three angles? Give reason for your answer.

In Fig.6.6, which of the two lines are parallel and why?

Two lines l and m are perpendicular to the same line n. Are l and m perpendicular to each other? Give reason for your answer.

In Fig. 6.9, OD is the bisector of ∠AOC, OE is the bisector of ∠BOC and

In Fig. 6.10, ∠1 = 60° and ∠6 = 120°. Show that the lines m and n are parallel.

AP and BQ are the bisectors of the two alternate interior angles formed by the intersection of a transversal t with parallel lines l and m (Fig. 6.11). Show that AP || BQ.

If in Fig. 6.11, bisectors AP and BQ of the alternate interior angles are parallel, then show that l || m.

In Fig. 6.12, BA || ED and BC || EF. Show that ∠ABC = ∠DEF.

[Hint: Produce DE to intersect BC at P (say)].

In Fig. 6.13, BA || ED and BC || EF. Show that ∠ABC + ∠DEF = 180°

In Fig. 6.14, DE || QR and AP and BP are bisectors of ∠EAB and ∠RBA, respectively. Find ∠APB.

The angles of a triangle are in the ratio 2: 3: 4. Find the angles of the triangle.

A triangle ABC is right angled at A. L is a point on BC such that AL ⊥ BC. Prove that ∠BAL = ∠ACB.

Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other.

If two lines intersect, prove that the vertically opposite angles are equal.

Bisectors of interior ∠B and exterior ∠ACD of a ΔABC intersect at the point T. Prove that ∠BTC = ∠BAC.

A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.

Prove that through a given point, we can draw only one perpendicular to a given line.

[Hint: Use proof by contradiction]

Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other.

Prove that a triangle must have at least two acute angles.

In Fig. 6.17, ∠Q > ∠R, PA is the bisector of ∠QPR and PM ⊥ QR. Prove that ∠APM = (∠Q – ∠R).