The Unknown Angle in a Triangle
In total, a triangle has 3 angles. If we already know 2 angles of the triangle, with a unknown, we can work out that unknown angle by adding up the 2 known angles and then subtracting it from 180° (all triangle add up to 180°).
Examples:
![Picture](/uploads/2/3/4/0/23408802/3049367.png)
1. Find the value of a in the triangle.
*all angles of a triangle equal 180°*
Solution
180 = 65 + 39 + a (angle sum of ∆ABC)
= 104 + a
a = 180 - 104
= 76
∴ a = 76°
*all angles of a triangle equal 180°*
Solution
180 = 65 + 39 + a (angle sum of ∆ABC)
= 104 + a
a = 180 - 104
= 76
∴ a = 76°
![Picture](/uploads/2/3/4/0/23408802/9596332.png)
2. Find the value of y in this triangle.
*isosceles triangles have 2 equal sides*
Solution:
180° = 70 + 70 + y
= 140 + y
y = 180 - 140
= 40
∴ y = 40°
*isosceles triangles have 2 equal sides*
Solution:
180° = 70 + 70 + y
= 140 + y
y = 180 - 140
= 40
∴ y = 40°
Quiz
1. Calculate the unknown angle in each of the triangles below: