1. **State the problem:** We have a circle divided into 5 sectors by radii from the center, with points A, B, C, D, and E on the circumference. Given: - Angle at point A is 52° - Measure of arc EA is 142° - Measure of arc BDC is 142° We need to find the measures of arcs ED and EA. 2. **Recall circle properties:** - The total measure of a circle is 360°. - The measure of arcs around the circle must sum to 360°. - The measure of an arc is the angle it subtends at the center. 3. **Calculate missing arcs:** - Given mEA = 142° and mBDC = 142°. - The arcs EA and BDC together cover part of the circle. 4. **Find mED:** - Since the circle is divided into arcs EA, ED, and BDC, their sum is 360°. - So, $$mEA + mED + mBDC = 360$$ - Substitute known values: $$142 + mED + 142 = 360$$ - Simplify: $$\cancel{142} + mED + \cancel{142} = 360$$ - $$284 + mED = 360$$ - Subtract 284 from both sides: $$mED = 360 - 284 = 76$$ 5. **Final answers:** - $$mED = 76^\circ$$ - $$mEA = 142^\circ$$