We appreciate your visit to In the diagram below of circle C mQT 140 and m. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Given:
Angle P is formed by two secants intersecting outside of circle C.
The intercepted arcs are major arc QT and minor arc RS.
[tex]\hat{mQT}=140\degree\text{ and }m\angle P=40\degree[/tex]Required:
[tex]\text{ We need to find }m\mathring{RS}.[/tex]Explanation:
Recall that
[tex]\text{ Angle Formed by Two Secants =}\frac{1}{2}(\text{ \lparen Difference of Intercepted Arcs\rparen}[/tex][tex]m\angle P=\frac{1}{2}(m\hat{QT}-m\hat{RS})[/tex][tex]Substitute\text{ }\hat{mQT}=140\degree\text{ and }m\angle P=40\degree\text{ in the equation.}[/tex][tex]40\degree=\frac{1}{2}(140\degree-m\hat{RS})[/tex]Multiply both sides by 2.
[tex]2\times40\degree=2\times\frac{1}{2}(140\degree-m\hat{RS})[/tex][tex]80\degree=140\degree-m\hat{RS}[/tex][tex]Add\text{ }m\hat{RS}-80\degree\text{ on both sides of the equation.}[/tex][tex]80\degree+m\hat{RS}-80\degree=140\degree-m\hat{RS}+m\hat{RS}-80\degree[/tex][tex]m\hat{RS}=140\degree-80\degree[/tex][tex]m\hat{RS}=60\degree[/tex]Final answer:
[tex]m\hat{RS}=60\degree[/tex]Thanks for taking the time to read In the diagram below of circle C mQT 140 and m. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
Rewritten by : Barada
