Answer:
mABC = 59°
Explanation:
To find the value of x, we can call the height BD by 'h' and then use the Pythagoras' theorem in the triangles ABD and BCD:
triangle ABD:
(3x + 1)^2 = (x + 1)^2 + h2
9x2 + 6x + 1 = x2 + 2x + 1 + h2
h2 = 8x2 + 4x
triangle BCD:
(4x - 1)^2 = (2x + 1)^2 + h2
16x2 - 8x + 1 = 4x2 + 4x + 1 + 8x2 + 4x
4x2 - 16x = 0
x2 - 4x = 0
x - 4 = 0
x = 4 units
Now we can find the angles mABD and mBDC using the sine relation:
sin(mABD) = (x + 1) / (3x + 1) = 5 / 13
mABD = 22.62°
sin(mBDC) = (2x + 1) / (4x - 1) = 9 / 15
mBDC = 36.87°
So we have that:
mABC = mABD + mBDC = 22.62° + 36.87° = 59.49°
Rounding to the nearest degree, we have mABC = 59°