Question

A city is planning to start construction of a new street. The new street will be named Elm street and is represented by the red dashed line in the diagram. Oak street, Maple street, and Cherry street are parallel to each other. If Elm street is constructed so that it is parallel to Oak, Maple, and Cherry, what will be the measure of angle 2? A. 130 degrees B. 120 degrees C. 60 degrees D. 50 degrees

Answer 1

Consecutive Interior Angles add up to 180°
Hence,
Angle 2 is consective interior angle to the angle 50°
Thus,
Angle 2= 180-50 = 130°
See the attachment for complete workout.
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Answer 2

the picture in the attached figure

Since the lines are parallel, we know that angle
`2` must be equal to
`130`°
Reason--------> by corresponding angles

Therefore,

the answer is the option
A.
`130` degrees

Alternative Method

Since the lines are parallel, we know that angle
`3` must be supplementary to
`130`°.
Therefore,
the measure of angle
`3` will be

`angle3+130=180 \\ angle 3=180-130 \\ angle3=50degrees`

we know that angle
`3` must be supplementary to angle
`2`

`angle3+angle 2=180 \\ 50+angle2=180 \\ angle2=180-50 \\ angle2=130 degrees`

Therefore,

the answer is the option
A.
`130` degrees

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