Question

You are given that the measure of angle NMP is 46 degrees and measure of angle PNQ is 27 degrees. Find the measure of angle MNP

Answer 1

m<MNP = 106°

Explanation:

Given:

m<NMP = 46°

m<PNQ = 27°

Required:

m<MNP

Solution:

Based on SAS Triangle Congruence Theorem (Side-Angle-Theorem), ∆NMP ≅ ∆PQN

Therefore:

m<NMP = 47°

m<MPN = 27° (<PNQ ≅ <MPN)

m<MNP + m<NMP + m<MPN = 180° (sum of interior angles of a triangle)

m<MNP + 47° + 27° = 180° (substitution)

m<MNP + 74° = 180°

Subtract 74 from both sides

m<MNP = 180° - 74°

m<MNP = 106°