Geometry Angle Problems Solution
The image displays two geometry problems, with accompanying figures, asking to find the measures of the marked angles.
For the first problem (A):
1. m∠ACD = (4x + 8)°
2. m∠ACB = (2x)°
To solve for x, use the fact that ∠ACB and ∠ACD are supplementary angles (since they form a straight line together), so their measures add up to 180 degrees:
(4x + 8)° + (2x)° = 180°
6x + 8 = 180
6x = 172
x = 28.67° (approximately)
Now you can find the measure of ∠ACD using the value of x:
m∠ACD = (4x + 8)° = (4*28.67 + 8)° = 122.67° (approximately)
For the second problem (B):
1. m∠BCD = (3x + 11)°
2. m∠ACD = (5x)°
Again, ∠BCD and ∠ACD are supplementary angles, so their total measure is 180 degrees:
(3x + 11)° + (5x)° = 180°
8x + 11 = 180
8x = 169
x = 21.125° (approximately)
Now you can find the measure of ∠ACD:
m∠ACD = (5x)° = (5*21.125)° = 105.625° (approximately)
So, for each problem, we have found the measures of the respective marked angles using the properties of supplementary angles.
