Angle Pairs Unit Test
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Question
Use the image to answer the question.
An illustration shows a slanting line intersecting with two lines that appear parallel. The angles that the slanting line forms with the top line are labeled from the top left in a clockwise direction as 1, 2, 4, and 3. The angles that the slanting line forms with the bottom line are labeled from the top left in a clockwise direction as 5, 6, 8, and 7.
m∠5=112° and m∠8=(2x+8)° . What equation will solve for x ?
(2 points)
x°+
°=
°
To find the value of x, we need to set up an equation using the given information:
m∠5 = 112°
m∠8 = (2x + 8)°
Since angles 5 and 8 are corresponding angles (they are in the same position on parallel lines intersected by a transversal), they are congruent.
So we can set up the equation:
m∠5 = m∠8
112° = (2x + 8)°
Now we can solve for x. Subtract 8 from both sides of the equation:
112° - 8° = 2x + 0°
104° = 2x
Divide both sides of the equation by 2:
104°/2 = 2x/2
52° = x
Therefore, the equation that will solve for x is:
x = 52°