Idon't understand!

< 1 and < 2 are linear pair. m< 1=x-30, and m< 2=x+76. find the measure of each angle?

1) < 1=67,< 2=123
2)< 1=37,< 2=153
3)< 1=37,< 2=143
4)< 1=67,< 2=113

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.

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.