Question
A triangle with exterior angles is shown. A horizontal line intersects with a diagonal line. Another line connects the horizontal line to the diagonal line to form a triangle. The exterior angle at the top left of the triangle is 130 degrees. The exterior angle at the top right of the triangle is x degrees. The exterior angle at the bottom of the triangle is 134 degrees.
The value of x is _____.
84
96
132
264
The value of x is _____.
84
96
132
264
Answers
GPT-4o mini
To find the value of \( x \), we can use the property that the sum of the exterior angles of any triangle is always \( 360^\circ \).
Given the exterior angles:
- Top left angle: \( 130^\circ \)
- Top right angle: \( x^\circ \)
- Bottom angle: \( 134^\circ \)
We can set up the equation:
\[
130 + x + 134 = 360
\]
Now, let's simplify:
\[
264 + x = 360
\]
Subtract \( 264 \) from both sides:
\[
x = 360 - 264 = 96
\]
Thus, the value of \( x \) is \( 96 \).
The answer is \( 96 \).
Given the exterior angles:
- Top left angle: \( 130^\circ \)
- Top right angle: \( x^\circ \)
- Bottom angle: \( 134^\circ \)
We can set up the equation:
\[
130 + x + 134 = 360
\]
Now, let's simplify:
\[
264 + x = 360
\]
Subtract \( 264 \) from both sides:
\[
x = 360 - 264 = 96
\]
Thus, the value of \( x \) is \( 96 \).
The answer is \( 96 \).