Question

.find angle x
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Answer 1

Answer:

a) 70+70+y = 180 (ASP property of triangle)

consider the 3 rd angle of the triangle as y

140+y=180

hence y= 180-140=40

x+y=180(supplementery angle)

x+40=180

hence x = 180-40=140

b)120+y =180

consider the 3 rd angle of the triangle as y

hence y = 180-120 = 60

x+y+70 =180  (ASP property of triangle)

x+60+70=180

x+130=180

hence x = 180-130 = 50

c) the other angle will be equal to x

2x+40 = 180

2x =180-40 = 140

hence x = 140/2

               = 70

d) the other angle will be equal to x

2x+90 = 180

2x = 180-90 = 90

hence x = 90/2 =45

e) all sides are equal hence all the angles will be equal

hence 3x =  180

x = 180 /3 = 60

Note - Add the degree symbol by yourself

Answer 2

a) In ∆ ABC,

< A = 70° < B = 70° < C = y°

Now,

Sum of all angles of a ∆ = 180°

< A + < B + < C = 180°

70° + 70° + y° = 180°

140° + y° = 180°

y° = 180° - 140°

y° = 40°

Now,

y° + x° = 180° ( Supplementary angles )

40° + x° = 180°,

x° = 180° - 40°

Therefore, x° = 140°

b) In ∆ ABC,

< A = x° < B = 70° < C = y°

To find < C,

<ACB + <ACD = 180° (Supplementary angles)

y° + 120° = 180°

y° = 180° - 120°

Therefore, y° = 60°

Now,

Sum of all angles of a ∆ = 180°

< A + < B + < C = 180°

x° + 70° + 60° = 180°

x° + 130° = 180°

x° = 180° - 130°

Therefore, x = 50°

c) ∆ ABC is a isosceles ∆.

< A = 40° < B = x° < C = x°

( because 2 sides and angles are equal in isosceles ∆ )

Now,

Sum of all angles of a ∆ = 180°

< A + < B + < C = 180°

40° + x° + x° = 180°

2x° = 180° - 40°

2x° = 140°

Therefore, x° = 140° / 2°

= 70°

d) ∆ ABC is a right-angled isosceles ∆.

< A = 90° < B = x° < C = x°

( because 2 sides and angles are equal in isosceles ∆ )

Sum of all angles of a ∆ = 180°

< A + < B + < C = 180°

90° + x° + x° = 180°

2x° = 180° - 90°

2x° = 90°

Therefore, x° = 90° / 2°

= 45°

e) ∆ ABC is a equilateral ∆.

< A = x° < B = x° < C = x°

( because all the sides and angles are equal in equilateral ∆ )

Sum of all angles of a ∆ = 180°

< A + < B + < C = 180°

x° + x° + x° = 180°

3x° = 180°

Therefore, x° = 180° / 3°

= 60°

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