9514 1404 393
Answer:
(A, B, C, D) = (84°, 112°, 136°, 28°)
Step-by-step explanation:
The degree measures of the angles in terms of x are ...
A = 3x
B = 4x
C = 4x +24
D = x
The sum of the angle measures is 360 degrees, so we have ...
A +B +C +D = 360
3x +4x +(4x+24) +x = 360
12x = 336 . . . . subtract 24, collect terms
x = 28 . . . . . . . divide by 12
Then the angle measures are ...
m∠A = 3·28° = 84°
m∠B = 4·28° = 112°
m∠C = 112°+24° = 136°
m∠D = 28°
