Answer:
m∠RMT = 48.5°
m∠RMN = 131.5°
m∠TMP = 131.5°
m∠NMP = 48.5°
Step-by-step explanation:
∠NMP and ∠PMT are supplementary angles.
Supplementary angles add up to 180°. Therefore we have the equation:
x + (3x - 14) = 180
x + 3x - 14 = 180 add 14 to both sides
4x = 194 divide both sides by 4
x = 48.5
∠NMP and ∠RMT are vertical angles. The vertical angles are equal. Therefore m∠NMP = m∠RMT.
m∠NMP = x° → m∠NMP = m∠RMT = 48.5°
∠TMP and ∠RMN are vertical angles. Therefore m∠TMP m∠RMN.
m∠TMP = (3x - 14)° → m∠TMP = m∠RMN = (3 · 48.5 - 14)° = 131.5°
