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Question

Given that lines m and n are parallel, find the measure of 1.


A
144°
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B
121°
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C
153°
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D
105°
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Solution

The correct option is A 144°
We know that if a transversal intersects two parallel lines, then the alternate exterior angles will be equal.
x2=x+30
x2x30=0
x26x+5x30=0
(By splitting the middle term of quadratic equation)
Taking the common factors out, we get
x(x6)+5(x6)=0
(x6)(x+5)=0
x=6 or x=5

Since the measure of an angle cannot be negative, consider the positive root x=6

We know that angles on a straight line sum up to 180.

x2+1=180 (Linear pair)
(62)+1=180
36+1=180
1=18036
1=144

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