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In ΔMNO, \overline{MO} MO is extended through point O to point P, \text{m}\angle NOP = (7x-17)^{\circ}m∠NOP=(7x−17) ∘ , \text{m}\angle MNO = (x+20)^{\circ}m∠MNO=(x+20) ∘ , and \text{m}\angle OMN = (3x-7)^{\circ}m∠OMN=(3x−7) ∘ . Find \text{m}\angle NOP.M∠NOP

Respuesta :

Answer:

∠NOP = 53°

Step-by-step explanation:

According to exterior angle theorem,

In a triangle, an exterior angle is equal to the sum of the two opposite interior angles.

∠NOP = ∠MNO + ∠OMN

Put ∠NOP = ( 7x - 17)°, ∠MNO = (x + 20)° and ∠OMN = (3x - 7)°

[tex]7x-17=x+20+3x-7\\7x-17=4x+13\\7x-4x=13+17\\3x=30\\x=10[/tex]

Therefore,

∠NOP = ( 7(10) - 17)° = (70 - 17)° = 53°

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