Q19 of 153 Page 166

Of the three angles of a triangle, one is twice the smallest and another one is thrice the smallest. Find the angles.

Let x be the common multiple.

So, angles will be x, 2x and 3x

X + 2x + 3x = 180

6x = 180

X =30

2x = 2 X 30 = 60

3x = 3 X 30 = 90

So, Angles are 30^O,60^O and 90^O

In the given figure AB || CD, ∠APQ = 50° and ∠PRD = 120°. Find ∠QPR.

In the given figure, BE is the bisector of ∠B and CE is the bisector of ∠ACD.

Prove that

In ΔABC, sides AB and AC are produced to D and E respectively. BO and CO are the bisectors of ∠CBD and ∠BCE respectively. Then, prove that

In ΔABC, ∠B = 90° and BD ⊥ AC. Prove that ∠ABD = ∠ACB.