Question

Find the value of x.

Answer 1

x = 40°

Explanation:

Measure of external angle outside a circle = ½ of the difference of the measurements of the intercepted arcs

Thus:

m<T = ½(arc PQ - arc RS)

x/2 = ½[(x + 70) - (x + 30)]

Multiply both sides by 2

x = (x + 70) - (x + 30)

x = x + 70 - x - 30 (distributive property)

Add line terms

x = x - x + 70 - 30

x = 40°