Question

Use the figure shown.

The diagram is two triangles opposite to each other. The left triangle angles are 46 degree, 51 degree, and y degree. The y degree angle is joined to the right side angle. The remaining two angles of right side triangle are x degree and 38 degree. The shape of the two triangles is like X.

What is the value of x?
A. 38
B. 59
C. 83
D. 96

Answer 1

To solve for the value of \(x\) in the triangles described, we can use the properties of triangles.

1. In the left triangle, the angles are 46 degrees, 51 degrees, and \(y\) degrees. The sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation:

\[
46 + 51 + y = 180
\]

2. Simplifying this gives:

\[
97 + y = 180
\]

3. Solving for \(y\):

\[
y = 180 - 97 = 83
\]

Thus, \(y = 83\) degrees.

4. Now, consider the right triangle, which has angles \(x\) degrees, 38 degrees, and \(y\) degrees (which we found to be 83 degrees). The sum of the angles in this triangle is also 180 degrees:

\[
x + 38 + 83 = 180
\]

5. Simplifying this gives:

\[
x + 121 = 180
\]

6. Solving for \(x\):

\[
x = 180 - 121 = 59
\]

Thus, the value of \(x\) is \(59\) degrees.

The correct answer is **B. 59**.