Question

In a ABC shown below, side AC is extended to point D with m Z DAB= (180 – 3x) °, mZ B= (6x – 40) °, and m ZC = (x+20) °.

Whats the measure of angle BAC?

Answer 1

60°

Explanation:

Given :

DAB= (180 – 3x) °,

mZ B= (6x – 40) °, and

m ZC = (x+20) °.

DAB = mZ B + m ZC ( the exterior angle equal the sum of the two opposite interior angles)

180 - 3x = (6x - 40) + (x + 20)

180 - 3x = 6x - 40 + x + 20

180 - 3x = 6x + x - 40 + 20

180 - 3x = 7x - 20

180 + 20 = 7x + 3x

200 = 10x

x = 200/10

x = 20

Angle B = 6x - 40 = 6(20) - 40 = 120 - 40 = 80

Angle C = x + 20 = 20 + 20 = 40

BAC = 180 - (80 + 40) (SUM OF ANGLES IN A TRIANGLE)

BAC = 180 - 120

BAC = 60°