Question

In the diagram below of circle C, mQT = 140, and m

Answer 1

Given:

Angle P is formed by two secants intersecting outside of circle C.

The intercepted arcs are major arc QT and minor arc RS.

`\hat{mQT}=140\degree\text{ and }m\angle P=40\degree`

Required:

`\text{ We need to find }m\mathring{RS}.`

Step-by-step explanation:

Recall that

`\text{ Angle Formed by Two Secants =}(1)/(2)(\text{ \lparen Difference of Intercepted Arcs\rparen}`
`m\angle P=(1)/(2)(m\hat{QT}-m\hat{RS})`
`Substitute\text{ }\hat{mQT}=140\degree\text{ and }m\angle P=40\degree\text{ in the equation.}`
`40\degree=(1)/(2)(140\degree-m\hat{RS})`

Multiply both sides by 2.

`2*40\degree=2*(1)/(2)(140\degree-m\hat{RS})`
`80\degree=140\degree-m\hat{RS}`
`Add\text{ }m\hat{RS}-80\degree\text{ on both sides of the equation.}`
`80\degree+m\hat{RS}-80\degree=140\degree-m\hat{RS}+m\hat{RS}-80\degree`
`m\hat{RS}=140\degree-80\degree`
`m\hat{RS}=60\degree`

Final answer:

`m\hat{RS}=60\degree`