Question

8. What is the value of x in the diagram?

A
E
429
B
49
D
32°C

Answer 1

D.
`10^(\circ)`

Explanation:

Let the measure of minor arc
`AE` be
`\alpha` and the measure of minor arc
`BD` be
`\beta`.

Using the secant-secant theorem,
`(\alpha-\beta)/(2)=32 \implies \alpha-\beta=64^(\circ)`.

By the inscribed angle theorem,
`\alpha=84^(\circ)`.

Thus,
`\beta=20^(\circ)`.

By the inscribed angle theorem,
`x=10^(\circ)`.