Question

which pair of angles x and y are supplementary?
m∠x = 113
m∠y = 67
m∠x = 76
m∠y = 14
m∠x = 180
m∠y = 180
m∠x = 140
m∠y = 190

4 multiple choice 4 points
in the accompanying diagram, line a intersects line b.
what is the value of x?
10
90
−10
5

Explanation:

First Question (Supplementary Angles)

Step1: Define supplementary angles

Supplementary angles sum to $180^\circ$.

Step2: Test each option

• Option1: $113 + 67 = 180$
• Option2: $76 + 14 = 90$
• Option3: $180 + 180 = 360$
• Option4: $140 + 190 = 330$

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Second Question (Vertical Angles)

Step1: Identify vertical angles

Vertical angles are congruent, so set equal:
$x + 5 = 2x - 5$

Step2: Solve for $x$

Subtract $x$ from both sides:
$5 = x - 5$
Add 5 to both sides:
$x = 10$

Answer:

A. $m\angle x = 113$, $m\angle y = 67$