The b. m∠27= 82°. Therefore , b. m∠27= 82° is correct .
From the image, we can see that lines x and y are parallel lines cut by a transversal. We are given that m∠4 = 82°.
We can use the following information:
Alternate interior angles are congruent.
Corresponding angles are congruent.
Supplementary angles add up to 180°.
Step 1: Find the measure of angle 1.
Angle 1 and angle 4 are alternate interior angles, so they are congruent. Therefore, m∠1 = m∠4 = 82°.
Step 2: Find the measure of angle 27.
Angle 27 and angle 1 are corresponding angles, so they are congruent. Therefore, m∠27 = m∠1 = 82°.
Step 3: Find the measure of angle 28.
Angle 28 and angle 4 are supplementary angles, so they add up to 180°. Therefore, m∠28 = 180° - m∠4 = 180° - 82° = 98°.
Therefore, the following is true:
m∠3 = 82° (alternate interior angles)
m∠7 = 82° (corresponding angles)
m∠8 = 98° (supplementary angles)
The answer is b. m∠7 = 82°.
Question
Lines x and y are parallel lines cut by 1 poin a transversal. If m∠ 4=82° , which of the following is true?
a. m∠ 3=82°
b. m∠ 7=82°
c. m∠ 8=82°
d. m∠ 5=82°