In triangle ABC, AX = XY = YB = BC and the measure of angle ABC is 150 degrees. What is the number of degrees in the measure of angle BAC?
+128475 Since BY = BC
Let angles BCY and BYC = x = angle BCA
Then angle YBC = 180 - 2x
And angle XBY = 150 - (180 - 2x) = 2x - 30 = Angle BXY
And since AX = XY
The angles XAY and XYA are equal
And by the exterior angle theorem, angle BXY = 2* angle XAY= angle BAC
2 * angle BAC = angle BXY
2 * angle BAC = 2x - 30
angle BAC = (2x - 30) / 2 = x - 15
So
angle BAC + angle ABC + angle BCA = 180
(x - 15) + ( 150 ) + (x) = 180
2x + 135 = 180
2x = 180 - 135
2x = 45
x = 22.5
Angle BAC = 22.5 - 15 = 7.5°
