a side of the triangle below has been extended to for an exterior angle of 161 find the value of x
leg length: 46
bottom length: 90
extended exterior: 161
leg length b: x
To solve this problem, we can use the property that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it.
Let's call the angles of the triangle A, B, and C. Angle C is the exterior angle that is formed when the side of the triangle is extended.
We are given that angle C has a measure of 161 degrees.
We are also given that the lengths of the legs of the triangle are 46 and x, and the length of the base is 90.
Since we know that the sum of the measures of the interior angles of a triangle is 180 degrees, we can write the following equation:
B + C = 180 (eq. 1)
The measure of angle B is equal to 180 - 90 = 90 degrees, because angle B is a right angle.
Substituting this into equation 1, we can solve for angle C:
90 + C = 180
C = 180 - 90
C = 90 degrees
We're given that angle C has a measure of 161 degrees. Therefore, there is an error in the problem statement. There is no solution for this triangle with the given measures.