Question

Please solve this question...​

Answer 1

Answer:

b. 55

Step-by-step explanation:

15+2x+3=5x-60(sum of two opposite interior angles = exterior angle)

18+2x=5x-60

18+60=5x-2x

78=3x

x=78/3

x=26

2x+3=2(26)+3

52+3=55

Answer 2

Question:

Find ∠ABC

(a) 26

(b) 55

(c) 52

(d) None

Exterior Angle Property:

The Exterior Angle Property of a triangle states that the sum of two interior opposite angles equals to the exterior angle.

Given,

1st interior opposite angle = 15°

2nd interior opposite angle = (2x + 3)

Exterior Angle = (5x - 60)

Thus,

15° + (2x + 3) = (5x - 60)

15° + 2x + 3 = 5x - 60

15° + 3 + 2x = 5x - 60

18° + 2x = 5x - 60

2x - 5x = - 60 - 18°

- 3x = - 78

x = - 78 ÷ (- 3)

x = 26

Now,

∠ABC = (2x + 3)

= (2 × 26 + 3)

= 52 + 3

= 55

Verification,

LHS = 15° + (2x + 3)°

= 15° + (2 × 26 + 3)°

= 15° + (52 + 3)°

= 15° + 55°

= 70

RHS = (5x - 60)°

= (5 × 26 - 60)°

= (130 - 60)°

= 70°

LHS = RHS hence, verified.

Therefore,

The value of ∠ABC equals to (b) 55°

Hope it helps