3. Given: BAM is a right angle. If mBAM=4x+2, then solve for the value of x.

3. x = 17

4. a. m<NMP = 48°

b. m<NMP = 60°

Step-by-step explanation:

3. Given that <BAM = right angle, and

m<BAM = 4x + 22, set 90° equal to 4x + 22 to find x.

4x + 22 = 90

Subtract 22 from both sides

4x + 22 - 22 = 90 - 22

4x = 68

Divide both sides by 4

4x/4 = 68/4

x = 17

4. a. m<NMQ = right angle (given)

m<PMQ = 42° (given)

m<PMQ + m<NMP = m<NMQ (angle addition postulate)

42 + m<NMP = 90 (substitution)

m<NMP = 90 - 42 (subtracting 42 from each side)

m<NMP = 48°

b. m<NMQ = right angle (given)

m<NMP = 2*m<PMQ

Let m<PMQ = x

m<NMP = 2*x = 2x

2x + x = 90° (Angle addition postulate)

3x = 90

x = 30 (dividing both sides by 3)

m<PMQ = x = 30°

m<NMP = 2*m<PMQ = 2*30

m<NMP = 60°