For this specific problem, the measure of each angle would be <1=37, <2=143. The correct answer between all the choices given is the third choice or number 3. I am hoping that this answer has satisfied your query about and it will be able to help you, and if you’d like, feel free to ask another question.
Answer:
3) ∠1=37, ∠2=143
Step-by-step explanation:
A linear pair of angles are the adjacent angles which are formed by two intersecting lines.
We know that, the measure of a straight angle is 180 degrees,
Thus, the sum of linear pairs is equal to 180°,
Here, m∠1=x-30°, and m∠2=x+76°,
Where, ∠1 and ∠2 are linear pair,
⇒ m∠1 + m∠2 = 180°
⇒ x - 30° + x + 76° = 180°
⇒ 2x + 46° = 180°
⇒ 2x = 134°,
⇒ x = 67°,
Hence, m∠1 = 67°-30° = 37°,
m∠1 = 67°+76° = 143°
Option '3' is correct.
