Question
Find x
in the figure. (1 point)
An illustration shows a triangle with a left angle of 35 degrees, an angle at the right of 40 degrees, and a top angle labeled y. A line extending outward from y forms an exterior angle labeled x.
in the figure. (1 point)
An illustration shows a triangle with a left angle of 35 degrees, an angle at the right of 40 degrees, and a top angle labeled y. A line extending outward from y forms an exterior angle labeled x.
Answers
GPT-4o mini
To find the value of \( x \) in the triangle you described, we first need to determine the value of angle \( y \).
The sum of the interior angles in a triangle is always \( 180^\circ \). Given the triangle has angles \( 35^\circ \) and \( 40^\circ \), we can find \( y \) as follows:
\[
y = 180^\circ - (35^\circ + 40^\circ)
\]
\[
y = 180^\circ - 75^\circ
\]
\[
y = 105^\circ
\]
Now, knowing that \( x \) is the exterior angle, we can use the exterior angle theorem, which states that an exterior angle is equal to the sum of the two opposite interior angles. In this case, the opposite interior angles are \( 35^\circ \) and \( 40^\circ \).
Thus, we can calculate \( x \):
\[
x = 35^\circ + 40^\circ
\]
\[
x = 75^\circ
\]
Therefore, the value of \( x \) is \( 75^\circ \).
The sum of the interior angles in a triangle is always \( 180^\circ \). Given the triangle has angles \( 35^\circ \) and \( 40^\circ \), we can find \( y \) as follows:
\[
y = 180^\circ - (35^\circ + 40^\circ)
\]
\[
y = 180^\circ - 75^\circ
\]
\[
y = 105^\circ
\]
Now, knowing that \( x \) is the exterior angle, we can use the exterior angle theorem, which states that an exterior angle is equal to the sum of the two opposite interior angles. In this case, the opposite interior angles are \( 35^\circ \) and \( 40^\circ \).
Thus, we can calculate \( x \):
\[
x = 35^\circ + 40^\circ
\]
\[
x = 75^\circ
\]
Therefore, the value of \( x \) is \( 75^\circ \).
Use the properties of exterior angles of triangles to find angle b
.An illustration shows a right triangle. The right angle is at the left; the top angle is labeled a; and the angle on the right is labeled b. A line extending outward from angle a forms an exterior angle of 142 degrees.
.An illustration shows a right triangle. The right angle is at the left; the top angle is labeled a; and the angle on the right is labeled b. A line extending outward from angle a forms an exterior angle of 142 degrees.
Use the properties of exterior angles of triangles to find angle b
.An illustration shows a right triangle. The right angle is at the left; the top angle is labeled a; and the angle on the right is labeled b. A line extending outward from angle a forms an exterior angle of 142 degrees.
.An illustration shows a right triangle. The right angle is at the left; the top angle is labeled a; and the angle on the right is labeled b. A line extending outward from angle a forms an exterior angle of 142 degrees.