Q2 of 153 Page 166

In a ΔABC, if ∠A – ∠B = 40° and ∠B – ∠C = 10°, find the measure of ∠A, ∠B and ∠C.

A = B + 40

C = B – 10

A + B + C = 180

B + 40 + B + B – 10 = 180

3B + 30 = 180

3B = 180 – 30 = 150

B = 50^O

So, A = B + 40 = 90^O

C = B – 10 = 40^O

Match the following columns:

Column I	Column II
(a) In the given figure, ABC is a straight line. Then, ∠ACD = …..	(p) 110°
(b) In the given figure, ∠AOC = (2x – 10)° and ∠BOC = (3x – 10)°. Then, ∠AOD = …	(q) 85°
(c) In the given figure, side BC of ΔABC has been produced to D. If ∠A = 65° and ∠B = 60°, then ∠ACD = ?	(r) 72°
(d) In the given figure, AB \|\| DE, ∠CDE = 50° and ∠BAC = 45°, then ∠ACB = ….	(s) 125°

The correct answer is:

A. – …….., B. – ……….,

C. – ………, D. – ……….,

The angles of a triangle are in the ratio 3:2:7. Find the measure of each of its angles.

The side BC of ΔABC has been increased on both sides as shown. If ∠ABD = 105° and ∠ACE = 110°, then find ∠A.

Prove that the bisectors of two adjacent supplementary angles include a right angle.