1. The problem is to find the missing central angle of a puzzle piece that completes a circle and a semicircle from the given pieces with angles 70°, 32°, 136°, 58°, and a quarter circle (90°). 2. Recall that the total angle around a point in a circle is 360°. 3. The quarter circle angle is 90°. 4. Sum the given angles: $$70 + 32 + 136 + 58 + 90 = 386°$$. 5. Since 386° exceeds 360°, the pieces must be split into two groups: one forming a full circle (360°) and the other forming a semicircle (180°). 6. The semicircle is 180°, so the missing piece for the semicircle is: $$180 - (70 + 32) = 180 - 102 = 78°$$ 7. The full circle is 360°, so the missing piece for the circle is: $$360 - (136 + 58 + 90) = 360 - 284 = 76°$$ 8. Therefore, the missing pieces have central angles 78° for the semicircle and 76° for the circle. Final answer: The missing angles are 78° and 76° to complete the semicircle and circle respectively.