# Examples on Theorem 2

Examples on Theorem Two

Published on ginnyent.net on 21st May, 2019

Look at the two diagrams below.  In Fig 1, find α and β.

In Fig 2, find, a and b.

Solution for Fig. 1

Recall what theorem 1, says. You can refresh your memory by visiting theorem 1.

In triangle XYZ, 700 + 300 + α = 1800(Sum of the angles in a triangle)

1000 + α = 1800

α =  1800 -1000

= 800

The exterior angle of triangle XYZ is represented by β

α + β = 1800 (sum of the angles on a straight line)

Since we have got α, 800 + β = 1800

β = 1800-800

= 1000

Solution for Fig. 2

In triangle RST, a + 500 + b = 1800 (sum of the angles in a triangle), but we don’t know a and b; that is we have two unknowns.

The exterior angle of triangle RST is 1200, and we know that;

a + 500 = 1200 (exterior angle of a triangle  = sum of two opposite interior angles)

Therefore a = 1200 – 500

= 700.

Now that we have found a, let’s find b.

500 + a + b = 1800 (sum of the angles in a triangle)

500 + 700 + b = 1800

b= 1800 – (500 + 700)

= 1800 – 1200

b = 600