Question

4. Given that MMO is right, answer the following:Р(a) If MPV=49, find m_MVP.N(b) If m_MVP is twice m/PVQ, find m_NVP.M

Answer 1

a) Angle NMP = 58°

b) Angle NMP = 60°

Step-by-step explanation

We are told that Angle NMQ is a right angle, meaning that Angle NMQ = 90°

a) Angle PMQ = 42°, what is Angle NMP?

From the image, we can tell that

(Angle NMQ) = (Angle NMP) + (Angle PMQ)

90° = Angle NMP + 42°

Angle NMP = 90° - 42° = 58°

b) If Angle NMP is twice Angle PMQ, find Angle NMP.

Let Angle PMQ = x

Then Angle NMP = 2 (Angle PMQ) = 2x

From the image, we can tell that

(Angle NMQ) = (Angle NMP) + (Angle PMQ)

90° = 2x + x

90° = 3x

3x = 90°

Divide both sides by 3

(3x/3) = (90°/3)

x = 30°

Therefore, Angle PMQ = x = 30°

Angle NMP = 2 (Angle PMQ) = 2 (30°) = 60°

Hope this Helps!!!