Math / Geometry

Question2. The following diagram shows where a road intersects two parallel streets. At one intersection $\angle 2$ measures $120^{\circ}$ . What are the measures of $\angle 7$ and $\angle 8$ at the other intersection? How do you know? $\angle 7=120^{\circ}$ I know this because 2 was $\angle 8=60^{\circ}$ 6 then to 7 so than the answer then to 7 so than the answ is 7 the you subtract $180-120$ $=60^{\circ}$ $120^{\circ}$

Studdy Solution

STEP 1

1. The road intersects two parallel streets, forming two pairs of corresponding angles.
2. Corresponding angles are equal when a transversal intersects parallel lines.
3. The sum of angles on a straight line is $180^\circ$ .

STEP 2

1. Identify the relationship between the angles.
2. Calculate the measure of $\angle 7$ .
3. Calculate the measure of $\angle 8$ .

STEP 3

Identify the relationship between the angles. Since the streets are parallel and the road is a transversal, $\angle 2$ and $\angle 7$ are corresponding angles. Therefore, $\angle 7 = \angle 2$ .

STEP 4

Calculate the measure of $\angle 7$ . Since $\angle 2 = 120^\circ$ , and $\angle 7$ is a corresponding angle, we have:
$\angle 7 = 120^\circ$

STEP 5

Calculate the measure of $\angle 8$ . Since $\angle 7$ and $\angle 8$ are on a straight line, they are supplementary. Thus, their measures add up to $180^\circ$ :
$\angle 8 = 180^\circ - \angle 7$ $\angle 8 = 180^\circ - 120^\circ$ $\angle 8 = 60^\circ$
The measures of the angles are:
$\angle 7 = 120^\circ$ $\angle 8 = 60^\circ$

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