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Use the diagram below to find the given variablesM, N, P, Q, R, S, T U

Use the diagram below to find the given variablesM, N, P, Q, R, S, T U-example-1
User Plaureano
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1 Answer

2 votes

From The diagram in the question.

Step 1: To find M,

M + 90+ 60 = 180(sum of angle in a triangle)

M + 150= 180

M = 180 - 150

M = 30

Use similar reason,

40+ 90+N = 180

130 + N =180

Therefore, N = 50

Step; Using angle on a straight line

112 + x = 180

x = 180 - 112 = 68

Then, M + X + Y = 180

30 + 68 + Y = 180

98 + y = 180

Y = 180-98 = 82

Note that Y and X are vertically opposite angle

P = 82

Step 3 ;Find q

70 is a vetically opposite angle

p + q + 70 = 180 ( sum of angle in a triangle)

82 + q + 70 =180

152 + q = 180

q = 28

Step4 : To find T ( Note that Y is vertically opposite to T)

N + 68 + Y = 180 ( Sun of angle in a Triangle)

50 + 68+ T = 180

118 + T = 180

T = 180 - 62

T = 118

Step 5 ; Find r

using sum of angles in a triangle

90 + 50 + r = 180

140 + r = 180

r = 40

r is vertically opposite angle

r + s + 70 = 180

40 + s + 70 = 180

110 + s = 180

s = 70°

Step 6; find U

From t, using angle on a straight line

t+ a = 180 + a = 180

118 +a = 180 - 118= 62

s + 62 + v = 180

70 + 62 + v = 180

132 + v = 180

v= 48

then, V is vertically opposite

90 + u + v(vertically opposite) = 180

90 + u + 48 = 180

u = 180 - 138

u = 42°.

Therefore, M = 30°, N = 50°, p= 82°, Q= 28°, R = 40°, S =70°, T =118°, U = 42°

User GeertVc
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