1. Given: C= 2,4,6,8,10 D=4,8,12,16,20 A. Find AUB - Gauthmath

Step 1: Identify the corresponding sides. Since $$AB = 5.6$$AB=5.6 and $$OQ = 5.6$$OQ=5.6, $$AB$$AB corresponds to $$OQ$$OQ. Since $$\angle BAC = 62^\circ$$∠BAC=62∘ and $$\angle OQP = 41^\circ$$∠OQP=41∘, $$\angle BAC$$∠BAC does not correspond to $$\angle OQP$$∠OQP. Since the two triangles are congruent, $$AC$$AC corresponds to $$QP$$QP and $$BC$$BC corresponds to $$OP$$OP.

Step 2: Find $$p$$p. Since $$AC$$AC corresponds to $$QP$$QP, $$p = 5.1$$p=5.1.

Step 3: Find the angle corresponding to $$\angle BCA$$∠BCA. Since $$AB$$AB corresponds to $$OQ$$OQ and $$AC$$AC corresponds to $$QP$$QP, $$\angle BCA$$∠BCA corresponds to $$\angle QPO$$∠QPO.

Step 4: Find $$\angle QOP$$∠QOP. In $$\triangle OPQ$$△OPQ, $$\angle OQP + \angle QPO + \angle POQ = 180^\circ$$∠OQP+∠QPO+∠POQ=180∘, so $$41^\circ + \angle QPO + \angle POQ = 180^\circ$$41∘+∠QPO+∠POQ=180∘. Since $$BC$$BC corresponds to $$OP$$OP and $$AB$$AB corresponds to $$OQ$$OQ, $$\angle ACB$$∠ACB corresponds to $$\angle QPO$$∠QPO. Since $$AC$$AC corresponds to $$QP$$QP and $$AB$$AB corresponds to $$OQ$$OQ, $$\angle ABC$$∠ABC corresponds to $$\angle POQ$$∠POQ. Since $$\angle BAC = 62^\circ$$∠BAC=62∘, $$\angle QPO$$∠QPO corresponds to $$\angle BCA$$∠BCA, and $$\angle POQ$$∠POQ corresponds to $$\angle ABC$$∠ABC, then $$\angle POQ = 62^\circ$$∠POQ=62∘. $$41^\circ + \angle QPO + 62^\circ = 180^\circ$$41∘+∠QPO+62∘=180∘, so $$\angle QPO = 180^\circ - 41^\circ - 62^\circ = 77^\circ$$∠QPO=180∘−41∘−62∘=77∘.

Step 5: Find $$q$$q. Since $$\angle QPO = \angle BCA$$∠QPO=∠BCA, $$q = 77^\circ$$q=77∘.