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What is the value of x?

What is the value of x?-example-1

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Answer:

Explanation:

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This is not an ordinary question. It is a little tricky. The slanted line making one arm of the angle 2x has three angles making it up. One is unmarked. Call it y.

Equations

2x + 90 + y = 180

3x + y = 120 which we have to prove.

Solution

The lower right angle of the parallelogram and the 60 degree angle are supplementary. Label that angle as z.

z + 60 = 180 Subtract 60 from both sides

z + 60-60 = 180 - 60 Combine

z = 120

z = 3x + y Opposite angles of a parallogram are equal.

Hence 120 = 3x+y

Now to deal with 2x

2x + 90 + y = 180 All three angles make up the slanted line.

Subtract 90 from both sides

2x + 90-90 +y = 180-90 Combine

2x + y = 90

Now you have 2 equations for 2 unknowns. Lets write them together.

3x + y = 120

2x + y = 90 Subtract.

x = 30

Answer: x = 30

User Shushanth Pallegar
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