Final answer:
After calculating, the value of x is 8.5 when solving the equation ZD = 10x = 85°. None of the given options match this calculated value, indicating a possible error in the options provided.
Step-by-step explanation:
From the given information that MACB = ADCE, and angles ZA = 50°, ZC = 45°, and ZD = 10x, we need to find the value of x. Since MACB and ADCE are said to be equal, the sum of the angles in both triangles must be the same. In triangle MACB, we already know two angles (ZA and ZC), which means we can find the third angle ZB as follows:
ZB = 180° - ZA - ZC = 180° - 50° - 45° = 85°
Since triangle ADC is equal to triangle MACB, angle ZB must be equal to ZD, so we equate them:
ZD = ZB
10x = 85°
Dividing both sides by 10 to solve for x, we get:
x = 85° / 10 = 8.5
However, when we look at the options provided (A) 5, (B) 10, (C) 15, (D) 20, none of them match our calculation of 8.5. This seems to be a discrepancy in the provided options, therefore it is not possible to select the correct value for x from the options given.