Question

If the m<7 = 115 degrees, find the measure of <2

Answer 1

Answer:

The measure of $\angle 2$ is 115°.

Step-by-step explanation:

Now, assuming those angles are supplementary, then

$m\angle 7+ m \angle 2=180\°$

Beacuse, sumplementary angles sum 180\°, due to their position on a straight angle.

We know by given that $m \angle 7 =115\°$, replacing this value, we have

$115\°+ m\angle 2= 180\°\\m \angle 2=180\° - 115\°\\m \angle 2= 65\°$

Therefore, the measure of $\angle 2$ is 115°.

Answer 2

The measure of m<7 is equal to the measure of m<2 by alternate exterior angle. The measure of <2 is 115 degrees.

What are the angles formed by the transverse line cut by the transversal?

Angles formed by the transverse line cut by the transversal-

• Corresponding angle- Corresponding angle keeps the same position on two different parallel line when cut by transverse.
• Alternate interior angle- This angle made inside the parallel lines cut by the transversal.
• Alternate exterior angle- This angle made outside the parallel lines cut by the transversal.
• Supplementary angle- Angle which made on the same line. The sum of the supplementary angle is equal to the 180 degrees.

Given information-

Two parallel lines are shown in the given image (attached below).

Here the measure of angle of 7 is 115 degrees.

The angle 5 is the supplementary angle of the angle 7. Thus,

$\angle 5+\angle 7 =180\\\angle 5+115=180\\\angle 5=180-115\\\angle 5=65$

Thus the measure of angle 5 is 65 degrees.

Now again the angle 5 is the supplementary angle of the angle 3. Thus,

$\angle 3+\angle 5 =180\\\angle 3+65=180\\\angle 3=180-65\\\angle 3=115$

Thus the measure of angle 3 is 115 degrees.

The angle 3 and the angle 2 cuts by the same line at the opposite side. Thus, angle 3 is equal to the angle 2.

Hence. the measure of angle 2 is 115 degrees.

Learn more about the angles formed by the transverse line cut by transversal here;

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