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In the diagram, MQ//RS, < TUV = 70o and < RLV = 30o. Find the value of x....


Question

In the diagram, MQ//RS, < TUV = 70o and < RLV = 30o. Find the value of x.

Options

A) 150o

B) 110o

C) 100o

D) 95o

The correct answer is C.

Explanation:

L + 30o - 180o(Sum of < s on straight line)

L = 180o - 30o = 150o

L = q = 150o(opposite < s are equal)

y = b = 30o(alt. < s)

b + c = 180o(sum of < s on str. line)

30o + c 180

c = 180 - 30

c = 150o

b = a = 30o (opp < s are equal)

c = d = 150o (opp < s are equal)

a + k + 70o = 180o (sum of < s on \(\bigtriangleup\))

30o + k + 70o = 180

k + 100o = 180

k = 180 - 100

k = 80o

x + 80o = 180(sum of < s on straight line)

x = 180o - 80o

x = 100o


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Dicussion (1)

  • L + 30o - 180o(Sum of < s on straight line)

    L = 180o - 30o = 150o

    L = q = 150o(opposite < s are equal)

    y = b = 30o(alt. < s)

    b + c = 180o(sum of < s on str. line)

    30o + c 180

    c = 180 - 30

    c = 150o

    b = a = 30o (opp < s are equal)

    c = d = 150o (opp < s are equal)

    a + k + 70o = 180o (sum of < s on \(\bigtriangleup\))

    30o + k + 70o = 180

    k + 100o = 180

    k = 180 - 100

    k = 80o

    x + 80o = 180(sum of < s on straight line)

    x = 180o - 80o

    x = 100o

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