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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

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 class=

Respuesta :

akposevictor

Answer:

m<MNP = 106°

Step-by-step 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°

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