Question

Let m Z1=(3x)º, m 22=(5x-7)", m 23=(4x+15), and m ZAFD=128º. Find m44 and m ZBFD.​

Answer 1

Answer:

m<4 = 52°

m<BFD = 98°

Step-by-step explanation:

m<1 = (3x)°

m<2 = (5x - 7)°

m<3 = (4x + 15)°

m<AFD = 128°

✔️Find m<4:

m<4 = 180° - m<AFD (angles on a straight line)

Substitute

m<4 = 180° - 128°

m<4 = 52°

✔️m<BFD = m<2 + m<3

Substitute

m<BFD = (5x - 7)° + (4x + 15)°

We need to find the value of x.

Create an equation to find x.

m<1 + m<2 + m<3 = m<AFD (angle addition postulate)

Substitute

3x + 5x - 7 + 4x + 15 = 128°

Add like terms and solve for x

12x + 8 = 128

12x + 8 - 8 = 128 - 8

12x = 120

12x/12 = 120/12

x = 10

m<BFD = (5x - 7)° + (4x + 15)°

Plug in the value of x

m<BFD = 5(10) - 7 + 4(10) + 15

m<BFD = 50 - 7 + 40 + 15

m<BFD = 98°