Question

Which statements about the diagram are true? Select three options.

x = 63
y = 47
z = 117
x + y = 180
x + z = 180

Answer 1

Answers are 1,3, and 5

Answer 2

• x = 63
• z = 117
• x + z = 180

Explanation:

x is a "corresponding" angle for the one marked 63°. Here, corresponding angles are congruent, so x = 63°.

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x and z are "same-side interior angles," so are supplementary. Their sum is 180°. x + z = 180°.

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Because x and z are supplementary and z and 63° are supplementary, you know that ...

z = 180° -63°

z = 117°

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Comments on the other answer choices

The value of y can be computed using the fact that the sum of angles interior to the triangle is 180°. The unmarked triangle interior angle is a vertical angle to the one labeled 63°, so it is 63°. Then the value of y is ...

y° = 180° -47° -63° = 70° . . . . . . . not 47°

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We already know that 63° + y + 47° = 180° and x = 63°. That means ...

x + y + 47° = 180°

so it cannot be true that x+y = 180.