Question

PROBLEMS
1. (b) In AABC, 2A + 2B = 65° and 2B + C = 140°. Find the measurement of each angle of the
triangle
(11) In a AABC, ZA - B = 33° and 2B - C = 18°. Find the measurement of each angle of the
triangle
(ix) The angles of a triangle are in the ratio 2 : 4:3. Find the measurement of the greatest angle,
(CBSE 2012)
(iv) An exterior angle of a triangle is 105º and its two interior opposite angles are equal. Find each
of the equal angles.
(o) One of the angles of a triangle is 75°. If the difference of the other two angles is 35º. Find the
[CBSE 2010
other two angles,​

Answer 1

Answer:

b) ∠A = 40 , ∠B = 25 and ∠C = 115

11) C = 37° A = 88° B = 55°

Step-by-step explanation:

Question (b)

∠A + ∠B = 65

∠B + ∠C = 140

∠A + ∠B + ∠B + ∠C = 65 + 140

(∠A + ∠B + ∠C) + ∠B = 205

180 + ∠B = 205

∠B = 205 - 180

∠B = 25°

∠C = 140 - ∠B

∠C = 140 - 25

∠C = 115°

∠A = 65 - ∠B

∠A = 65 - 25

∠A = 40°

Therefore  

∠A = 40° , ∠B = 25° and ∠C = 115°

Question 11)

Given A-B = 33

So A = 33+B.........(i)

B-C = 18

C = B-18...........(ii)

In a triangle

A+B+C = 180

33+B+B+B-18 = 180 ( FROM i and ii)

3B+15 = 180

3B = 165

B = 165/3

B = 55°

From i

A = 33+B

A = 33+55

A = 88°

From ii

C = B -18

C = 55-18

C = 37°