Answer:
68°
Explanation:
BA and BD are perpendicular, so that makes a 90° angle.
If we add m∠ABC and m∠CBD we get 90°, and can solve for m∠CBD.
So:
m∠ABC + m∠CBD = 90°
4x + 52 + 8x - 10 = 90 Combine like terms
4x + 8x + 52 - 10 = 90
12x + 42 = 90 Subtract 42 from each side
12x + 42 - 42 = 90 - 42
12x = 48 Divide each side by 12
12x/12 = 48/12
x = 48/12
x = 4
Now that we've solved for x we can plug it into m∠CBD and solve.
4x + 52 = ??
4(4) + 52 = ??
16 + 52 = 68
m∠CBD = 68°