Question

if m∠2 = 137 and m∠p = 22, what is m∠o? 43 115 21 65

Explanation:

Step1: Find m∠1 (supplementary angles)

∠1 and ∠2 are supplementary, so \( m\angle1 = 180^\circ - m\angle2 \).
\( m\angle1 = 180 - 137 = 43^\circ \).

Step2: Find m∠O (triangle angle sum)

In triangle \( OHP \), the sum of angles is \( 180^\circ \). So \( m\angle O = 180^\circ - m\angle1 - m\angle P \).
\( m\angle O = 180 - 43 - 22 = 115^\circ \)? Wait, no—wait, recalculate: \( 180 - 43 = 137 \), \( 137 - 22 = 115 \)? Wait, no, wait: Wait, ∠1 is 43, ∠P is 22, so ∠O = 180 - 43 - 22 = 115? Wait, but let's check again. Wait, maybe I made a mistake. Wait, ∠2 is 137, so ∠1 is 180 - 137 = 43. Then in triangle OHP, angles are ∠1 (43), ∠P (22), and ∠O. So 43 + 22 + ∠O = 180. So ∠O = 180 - 43 - 22 = 115? Wait, but the options include 115? Wait, the options are 43, 115, 21, 65. Wait, maybe I messed up. Wait, no—wait, maybe ∠1 is an exterior angle? Wait, no, ∠2 and ∠1 are adjacent and form a linear pair, so they are supplementary. Then triangle angle sum: sum of interior angles is 180. So ∠O = 180 - ∠1 - ∠P = 180 - 43 - 22 = 115. Wait, but let me check again. 43 + 22 = 65, 180 - 65 = 115. Yes. So m∠O is 115? Wait, but the options have 115. Wait, but maybe I made a mistake. Wait, no—wait, the problem: ∠2 is 137, so ∠1 is 43. Then in triangle OHP, angles at H (∠1=43), at P (22), so angle at O is 180 - 43 - 22 = 115. So the answer is 115? Wait, but let me check the options again. The options are 43, 115, 21, 65. So 115 is an option. Wait, but maybe I messed up the triangle. Wait, the triangle is OHP, with H on the line, so ∠1 is at H, between OH and HP, and ∠2 is adjacent to ∠1, forming a linear pair. So yes, ∠1 = 180 - 137 = 43. Then triangle angle sum: 43 + 22 + ∠O = 180 → ∠O = 115. So the answer is 115.

Answer:

115