Suppose you construct a figure with PR tangent to drcle Q at R and PS tangent to circle Q at S. Complete the conjecture about ZP and 2Q, and the explanation for the conjecture. The angles ZP and ZQ are ? v angles. The sum of the angle measures in quadrilateral PRQS is perpendicular to a radius, ZR and S are right angles. °. Since a line tangent to a circle is By substitution, mZP+ mZR +mZQ +mS =mZP+ So, mZP +mZQ = 180°. So, mZP and m2Q are ? P+mzQ + P- 360°. v angles. P.

5. If 2JEL and are adjacent angles, then ZJEL +ZLEO- 180°. PERFORMANCE TASKS: Direction: In the given figure, GRAYis a rectangle. Complete the conclusion and write the reasons that will justify each of the statements. Y. 1. If Sis the midpoint of GA, then 2. If GA bisects RY, then 3. If GR is perpendicular to RA , 4. If ZGRA and ZRAY are supplementary angles, then then 5. If ZGYS and ZSYA formed a right angle, then SCHOOLS DIV Bridging learners to a brighter future. I CAGAYAN DE

2. Find the missing angles labelled in each of these circles. a. 31° b. Ý SOE BỘ 80+2 90-y 2x+4 C. 12cm Scmy