1. **Problem Statement:** Find the measures of the arcs in the two circles as given. 2. **Given Data:** - First circle points: D, E, M, K, L - Angles and arcs: angle between KL and line from E is 26° - Arcs to find: $mDL=90^\circ$, $mEM=52^\circ$, $mEK=116^\circ$, $mLDM=154^\circ$ - Second circle points: P, T, H, G, C, V, R - Angle at T between arcs TH and TG is 30° - Arcs to find: $mVC=120^\circ$, $mPR=180^\circ$, $mPV=120^\circ$, $mTRC=240^\circ$ 3. **Step-by-step solution for the first arc $mDL=90^\circ$:** - This is given directly as $90^\circ$. 4. **Step-by-step solution for the second arc $mEM=52^\circ$:** - Given directly as $52^\circ$. 5. **Step-by-step solution for the third arc $mEK=116^\circ$:** - Given directly as $116^\circ$. 6. **Step-by-step solution for the fourth arc $mLDM=154^\circ$:** - Given directly as $154^\circ$. 7. **Step-by-step solution for the fifth arc $mVC=120^\circ$:** - Given directly as $120^\circ$. 8. **Step-by-step solution for the sixth arc $mPR=180^\circ$:** - Given directly as $180^\circ$. 9. **Step-by-step solution for the seventh arc $mPV=120^\circ$:** - Given directly as $120^\circ$. 10. **Step-by-step solution for the eighth arc $mTRC=240^\circ$:** - Given directly as $240^\circ$. **Summary:** All arc measures are given explicitly in the problem statement or figure description, so no further calculation is needed. **Final answers:** - $mDL=90^\circ$ - $mEM=52^\circ$ - $mEK=116^\circ$ - $mLDM=154^\circ$ - $mVC=120^\circ$ - $mPR=180^\circ$ - $mPV=120^\circ$ - $mTRC=240^\circ$