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 y?
A. 83
B. 89
C. 96
D. 97
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 y?
A. 83
B. 89
C. 96
D. 97
Answers
GPT-4o mini
To find the value of angle \( y \) in the left triangle, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.
Given the angles in the left triangle:
- Angle 1: \( 46^\circ \)
- Angle 2: \( 51^\circ \)
- Angle 3: \( y \)
We can set up the equation:
\[
46 + 51 + y = 180
\]
Now, adding \( 46^\circ \) and \( 51^\circ \):
\[
97 + y = 180
\]
Next, subtract \( 97 \) from both sides to solve for \( y \):
\[
y = 180 - 97
\]
\[
y = 83
\]
So, the value of \( y \) is \( 83^\circ \).
Therefore, the correct answer is:
**A. 83**
Given the angles in the left triangle:
- Angle 1: \( 46^\circ \)
- Angle 2: \( 51^\circ \)
- Angle 3: \( y \)
We can set up the equation:
\[
46 + 51 + y = 180
\]
Now, adding \( 46^\circ \) and \( 51^\circ \):
\[
97 + y = 180
\]
Next, subtract \( 97 \) from both sides to solve for \( y \):
\[
y = 180 - 97
\]
\[
y = 83
\]
So, the value of \( y \) is \( 83^\circ \).
Therefore, the correct answer is:
**A. 83**