Find the measure of the three exterior angles
of a triangle if the measures of the three
angles of a triangle are as follows:
A. 55° 65 60°
B. 115, 350, 300
Answers
Answer:
Part A = 125°, 115°, 120°
Part B = 65°, 145°, 150°
Solution:
In Part A, the measure of the three angles of the triangle is 55°, 65° and 60°.
We know that that we get an exterior angle when we extend extend any side of a triangle. The interior angle and exterior angle together form a straight angle, that is, 180°.
Please refer attachment for diagrammatical representation.
Angle 1 = 55°
Interior angle + Exterior angle = 180°
55° + Exterior angle = 180°
Exterior angle = 180 - 55
= 125°
Angle 2 = 65°
Interior angle + Exterior angle = 180°
65° + Exterior angle = 180°
Exterior angle = 180 - 65
= 115°
Angle 3 = 60°
Interior angle + Exterior angle = 180°
60° + Exterior angle = 180°
Exterior angle = 180 - 60
= 120°
How to confirm?
The sum of all exterior angles of a triangle is 360°.
LHS = 125 + 115 + 120
LHS = 360°
RHS = 360°
LHS = RHS
Hence verified!!
In Part B too, the measure of the three angles are given as 115°, 35° and 30°.
We can apply the same method we used for Part A here:
Angle 1 = 115°
Interior angle + Exterior angle = 180°
115° + Exterior angle = 180°
Exterior angle = 180 - 115
= 65°
Angle 2 = 35°
Interior angle + Exterior angle = 180°
35° + Exterior angle = 180°
Exterior angle = 180 - 35
= 145°
Angle 3 = 30°
Interior angle + Exterior angle = 180°
30° + Exterior angle = 180°
Exterior angle = 180 - 30
= 150°
How to confirm?
The sum of all the exterior angles of a triangle is 360°.
LHS = 65 + 145 + 150
= 360°
RHS = 360°
LHS = RHS
Hence verified!!
