In the figure shown, what is the value of x ?
A. 60
B. 80
C. 85
D. 90
E. 95
We can label some of the angles by variables as shown above. Recall that the measure of an exterior angle of a triangle is the sum of the two remote interior angles. So we have:
150 = b + c
150 = a + b
150 = x + y
and
y = a + c
Add up these four equations, we have:
450 + y = 2a + 2b + 2c + y + x
450 = 2(a + b + c) + x
Notice that a + b + c = 180 since they are the interior angles of a triangle. So we have:
450 = 2(180) + x
450 = 360 + x
90 = x
Alternate Solution:
Referring to the figure above, since a and 150 are supplementary, a = 30. Similarly, since c and 150 are supplementary, c = 30. The third angle in the triangle with angles x and y is also 30 for the same reasons. Since the measure of an exterior angle of a triangle is the sum of the two remote interior angles, y = a + c = 60. Now, we have a triangle where the interior angles are x, y = 60 and 30; thus x + 60 + 30 = 180, which implies x = 90.
Answer: D
Attachment:
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