Question

Trapezoid ROCK is isosceles. Find m

Answer 1

Step-by-step explanation:

Since this trapezoid is isosceles, the upper angles are congruent and the bottom angles are congruent:

`\begin{gathered} \angle KCO\cong\angle\text{COR} \\ \angle CKR\cong\angle ORK \end{gathered}`

Therefore mAngles
`\begin{gathered} m\angle CKR=m\angle CKO+m\angle OKR \\ 120º=m\angle CKO+24º \\ m\angle CKO=120º-24º=96º \end{gathered}`We have that angle OKR is 24º and angle ORK is 120º. The sum of the measures of the interior angles of a triangle is 180º:

`\begin{gathered} m\angle OKR+m\angle ORK+m\angle ROK=180º \\ 24º+120º+m\angle ROK=180º \\ m\angle ROK=180º-24º-120º=36º \end{gathered}`

Angles ROC and KCO are congruent and by angle addition the measure of angle ROC is:

`m\angle ROC=24º+36º=60º`

Answers:

• m,• m,• m