Question

Determine the number of degrees in the arcs?

Answer 1

First, we find angle K

`\begin{gathered} m\angle K+90+56=180 \\ m\angle K=180-90-56=34 \end{gathered}`

Then, we use the inscribed angle theorem

`\begin{gathered} m\angle K=(1)/(2)\cdot PM \\ PM=2\cdot m\angle K=2\cdot34=68 \end{gathered}`

Hence, the arc PM measures 68°.

Also, the arc MP measures 68° because it's the same arc.

If arc MT is 170°, and MP is 68°, then

`PT=170-68=102`

Then, we observe that arc KTP is equal to 180° because it's half the circumference. So,

`\begin{gathered} KT+TP=KTP \\ KT+102=180 \\ KT=180-102=78 \end{gathered}`

Hence, arc KT measures 78°.