Answer:
Base angles = 40°
Vertex angle = 100°
Step-by-step explanation:
Look at the attached figure.
The external angle, is the angle outside the triangle. An isosceles angle has two base angles and a vertex angle. The base angles are congruent.
The external angle and one of the base angles (the one beside the external angle) are supplementary, this means that the sum of their angles is 180°.
With that, we can solve for one base angle:
base angle + external angle = 180°
base angle + 140° = 180°
base angle = 180° - 140°
base angle = 40°
So the base angles each have a measurement of 40°
Okay, now that we know this, we can solve for the , so there are two ways to do this.
I: The sum of the internal angles is equal to the external opposite them. Then the vertex angle + a base angle = external angle
vertex angle + 40° = 140°
vertex angle = 140° - 40°
vertex angle = 100°
The vertex angle is 100°.
OR YOU CAN DO THIS:
II. The sum of all angles in a triangle is equal to 180°.
Base angle + Base angle + Vertex Angle = 180°
40° + 40° + Vertex angle = 180°
80° + Vertex angle = 180°
Vertex angle = 180° - 80°
Vertex angle = 100°
