In the figure below, angle $$a = 51 ^ { \circ }$$ . Find $X$ .
A) 166
B) 39
C) 129
D) 78
E) 64

Question

In the figure below, angle $$a = 51 ^ { \circ }$$ . Find $X$ . 
A) 166 
B) 39 
C) 129 
D) 78 
E) 64

Quizplus · Accepted Answer

First, notice that angles $$a$$ and $$b$$ form a linear pair, meaning they add up to 180 degrees. Therefore, $$b = 180 - a = 180 - 51 = 129$$ degrees.

Next, notice that angles $$b$$ and $$c$$ are vertical angles, meaning they are equal. Therefore, $$c = b = 129$$ degrees.

Finally, notice that angles $$c$$ and $$d$$ form a linear pair, meaning they add up to 180 degrees. Therefore, $$d = 180 - c = 180 - 129 = 51$$ degrees.

Since triangle $$DEX$$ is isosceles, angles $$d$$ and $$e$$ are equal, meaning $$e = d = 51$$ degrees.

Finally, angles $$e$$ and $$f$$ form a linear pair, meaning they add up to 180 degrees. Therefore, $$f = 180 - e = 180 - 51 = 129$$ degrees.

Since angles $$h$$ and $$f$$ form a vertical angle with angle $$c$$, they are equal, meaning $$h = f = 129$$ degrees.

Finally, angles $$h$$ and $$X$$ form a linear pair, meaning they add up to 180 degrees. Therefore, $$X = 180 - h = 180 - 129 = 51$$ degrees.

Therefore, the answer is C) 129.

In the Figure Below, Angle a=51∘a = 51 ^ { \circ }a=51∘

In the Figure Below, Angle $a = 51 ^ { \circ }$