Q1 of 153 Page 166

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

Let x be the common multiple.

3x + 2x + 7x = 180

12x = 180

X = 15

3x = 45^o

2x = 30^o

7x = 105^o

Match the following columns:

Column I	Column II
(a) If x° and y° be the measures of two complementary angles such that 2x = 3y, then x=………..	(p) 45^o
(b) If an angle is the Supplement of itself, then then the measure of the angle is ………….	(q) 60^o
(c) If an angle is the complement of itself, then the measure of the angle is………….	(r) 54^o
(d) If x° and y° be the angles forming a linear pair such that x – y = 60°, then y = …	(s) 90^o

The correct answer is:

A. – …….., B. – ……….,

C. – ………, D. – ……….,

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. – ……….,

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

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