4. The length of overline (CB) is [(A)1(B)5(C)19] ,and mangle BDA is [ 490 (B)67 (C) 23]^circ

To solve this problem, we need to use the information provided in the picture details and the question to find the values of and .Step 1: Determine the value of x.We know that the sum of the angles in a triangle is 180 degrees. Therefore, in triangle ABC, we have: Given that , , and (since it's a right triangle at A), we can write:\((9x - 4) + (4x + 1) + 90 = 180\)Combining like terms: Subtract 87 from both sides: Divide by 13: (approximately)Step 2: Find the length of .Since and we have found that , we can calculate :\(\angle BCA = 4(7.15) + 1\) (approximately)However, we are given that . Since and are part of the same larger angle , we can find by adding them together: (approximately)Since is not a right angle, cannot be the hypotenuse of a right triangle, and thus, cannot be the longest side of triangle ACD. Therefore, the length of cannot be determined solely by the angles given. We need additional information to find the exact length of . However, the question provides possible lengths as [1, 5, 19], but without additional information, we cannot determine which one is correct.Step 3: Find .We are given that . Since is an extension of , and a straight line measures 180 degrees, we can find by subtracting from 180 degrees: However, none of the given options for match 157 degrees. It seems there might be a mistake in the question or the options provided. Based on the information given, we cannot match the answer to any of the provided options [90, 67, 23] degrees.Final Answer:The length of cannot be determined from the given information. The measure of is 157 degrees, which does not match any of the provided options.