In triangle ABC, AX = XY = YB = BC and the measure of angle ABC is 120 degrees. What is the number of degrees in the measure of angle BAC?

15

Step-by-step explanation:

Let t be the number of degrees in the measure of angle BAC (which is what we want to compute).

Since AX=XY, we have AYX = YAX = BAC = t. Then, since the sum of angles in triangle AXY is 180, we have AXY = (180-2t).

Angles AXY and BXY add to form a straight angle, so they are supplementary; BXY = (180-(180-2t)) = (2t).

Since XY=YB, we have XBY = XY = (2t). Since the sum of angles in XYB is 180, we have XYB = (180-4t).

Angles AYX,  XYB, and BYC add to form a straight angle, so their sum is 180. Therefore, BYC = (180-t-(180-4t)) = (3t).

Since YB=BC, we have YCB = BYC = (3t). Since the sum of angles in YBC is 180, we have YBC = (180-6t).

Finally, ABC = XBY + YBC = (2t) + (180-6t) = (180-4t). We know this is equal to 120, so we solve the equation 180-4t = 120 to obtain t=15.

ℓσℓ ιт ∂σит тяσυвℓє мє αт αℓℓ ιм gℓα∂ тσ нєℓρ ρρℓ συт

ωє ιт ¢αи вє ωяιттєи αѕ

step-by-step explanation:

нσρє ι ¢συℓ∂ нєℓρ уσυ συт