In Fig. 6.1, if AB || CD || EF, PQ || RS, ∠RQD = 25° and ∠CQP = 60°, then ∠QRS is equal to
(A) 85°
(B) 135°
(C) 145°
(D) 110°
If one angle of a triangle is equal to the sum of the other two angles, then the triangle is
(A) An isosceles triangle
(B) An obtuse triangle
(C) An equilateral triangle
(D) A right triangle
An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of
these equal angles is
(A) 37 ½°
(B) 52 ½°
(C) 72 ½°
(D) 75°
The angles of a triangle are in the ratio 5 : 3 : 7. The triangle is
(A) An acute angled triangle
(B) An obtuse angled triangle
(C) A right triangle
(D) An isosceles triangle
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 a 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. , OD is the bisector of ∠AOC, OE is the bisector of ∠BOC, and OD ⊥ OE. Show that the points A, O, and B are collinear.
In Fig. , ∠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. ). Show that AP || BQ.
If in Fig. , bisectors AP and BQ of the alternate interior angles are parallel, then show that l || m.
In Fig. , BA || ED and BC || EF. Show that ∠ABC = ∠DEF
If two lines intersect, prove that the vertically opposite angles are equal.
Bisectors of interior ∠B and exterior ∠ACD of a Δ ABC intersect at the point T.
Prove that ∠ BTC = ½ ∠ BAC.
A transversal intersects two parallel lines. Prove that the bisectors of any pair of corresponding angles so formed are parallel.
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