Answer:
None of the Above
Step-by-step explanation:
Key Skills required are: One Variable Equations, Supplementary Angle Pairs, Substitution, and Triangles.
1) To find the measure of Angle C, we first need to find the measure of angle DBC and Angle D.
2) We are given that Angle EBA is x and Angle EBD is 4x+13 and Angle D is 3x + 9 (we will use Angle D later in the problem)
3) Now, we need to use the fact that Angle EBA and Angle EBD are supplementary (they form a linear pair, so they are supplementary).
A pair of supplementary angles add up to 180 degrees (as they form a straight angle).
4) x + 4x + 13 = 180
5) Combine like terms --> 5x + 13 = 180
6) Move 13 to the other side --> 5x = 167
7) Divide by 5 and solve for x: x= 33.4
8) Now we got that x is 33.4, we can get the measure of angle DBC and Angle D.
9) Angle DBC is congruent to Angle EBA. So to find the measure of DBC we need to find the measure of Angle EBA. EBA is just x, so it is 33.4 degrees
10) Therefore, Angle DBC also measures 33.4 degrees.
11) To find angle D, we substitute x into 3x + 9 (We are given angle D is 3x + 9 based on the problem)
12) 3(33.4) + 9 = 100.2 + 9 = 109.2
13) Now we use the interior angles sum of a triangle to find Angle C.
The interior angles of a triangle sum up to 180 degrees.
14) With the statement above we can make this equation: 109.2 + 33.4 + Angle C = 180
15) Simplify by combining like terms: 142.6 + Angle C = 180
16) 37.4 degrees would be the measure of C, so I feel it would be none of the above.
Hope you understood and have a nice day!! :D
