Question - Geometry Angle Problems Solution
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 = 1806x = 172x = 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 = 1808x = 169x = 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.
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