The exterior angle at the vertex formed by the equal sides of an isoceles triangle is 140 degrees. Which are the measures of the exterior angles at the other verticies
A ) 140 degrees and 80 degrees
B ) 110 degrees and 110 degrees
C ) 40 degrees and 40 degrees
D ) 40 Degrees and 90 degrees
interior = 180 - 140 = 40
40 + 2 x = 180
2x = 140
x = 70
180 - x = 110
Which one is it?
Is it B?
To find the measures of the exterior angles at the other vertices of an isosceles triangle, we need to use the fact that the sum of all the exterior angles of any polygon is always 360 degrees.
In an isosceles triangle, the two equal sides will be opposite to the two equal angles. This means that the exterior angle at the vertex formed by the equal sides will be equal to the sum of the other two interior angles in the triangle.
Let's denote the measure of each of the other two interior angles as x. According to the given information, the measure of the exterior angle is 140 degrees. Therefore, we can set up the following equation:
x + x + 140 = 360
Simplifying the equation:
2x + 140 = 360
2x = 220
x = 110
So, the measure of each of the other two interior angles is 110 degrees.
Now, to find the measures of the corresponding exterior angles at the other vertices, we subtract the interior angles from 180 degrees, since the exterior and interior angles are supplementary. Thus, the measures of the exterior angles at the other vertices are:
180 - 110 = 70 degrees
Therefore, the correct answer is option B) 110 degrees and 110 degrees.