Answer: 133°
Step-by-step explanation:
The Triangle External Angle Theorem states that an exterior angle of a triangle is equal to the sum of the opposite interior angles.
Exterior angle = sum of opposite interior angles
x = 46 + 87
x = 133
WHY DOES THIS THEOREM WORK?
let "y" represent the unknown angle of the triangle.
Then x and y form a linear pair, which means they are supplemental angles ⇒ x + y = 180°
The triangle sum Theorem states that the sum of the angles of a triangle equal 180° ⇒ 46 + 87 + y = 180°
Now use the transitive property (both equations are equal to 180 so they are equal to each other) ⇒ x + y = 46 + 87 + y
Subtract y from both sides to get: x = 46 + 87
= 133
