A side of the triangle below has been extended to form an exterior angle of 70°. Find the value of x.
Left: 70. Right: 46.
Since the exterior angle is formed by extending one side of the triangle, it is equal to the sum of the two opposite interior angles.
Let's call the angle at the top vertex of the triangle A.
Since angle A is opposite the extended side, it has a measure of 70 degrees.
Let's call the angle at the left vertex of the triangle B.
Since angle B is adjacent to the extended side, it has a measure of 46 degrees.
The remaining angle at the right vertex of the triangle is angle C.
Since angles A, B, and C add up to 180 degrees, we can subtract angles A and B from 180 to find the measure of angle C:
Angle C = 180 - angle A - angle B = 180 - 70 - 46 = 64 degrees.
Since angles B and C are two interior angles of a triangle, we can use the triangle angle sum to find the measure of angle x:
Angle x = 180 - angle B - angle C = 180 - 46 - 64 = 70 degrees.
wrong.
Apologies for the incorrect response earlier. Let's solve the problem correctly.
Let's call the angle at the top vertex of the triangle A.
Since angle A is opposite the extended side, it has a measure of 70 degrees.
Let's call the angle at the left vertex of the triangle B.
Since angle B is adjacent to the extended side, it has a measure of 46 degrees.
We need to find the value of angle x, which is located at the right vertex of the triangle.
Since angles A, B, and x add up to 180 degrees, we can use the triangle angle sum to find the measure of angle x:
x = 180 - angle A - angle B = 180 - 70 - 46 = 64 degrees.
Therefore, the value of angle x is 64 degrees.
To find the value of x, we need to use the fact that the sum of the measures of the exterior angles of a triangle is always 360°.
In this case, since the given angle is an exterior angle, we can subtract it from 360° to get the sum of the other two interior angles of the triangle.
360° - 70° = 290°
The sum of the two interior angles of the triangle is 290°. Since we are given that one angle measures 46°, we can subtract it from 290° to get the measure of the other angle.
290° - 46° = 244°
Therefore, the value of x is 244°.