Points A and B split the circle into two arcs. Measure of minor arc is 150°. Point M splits major arc with the ratio 2:5 (point M is closer to point B). Find m∠BAM.
Accepted Solution
A:
Answer:∠BAM=30°Step-by-step explanation:Points A and B split the circle into two arcs. If the measure of minor arc AB is 150°, then the measure of the major arc AB is 360°-150°=210°.If point M splits major arc with the ratio 2:5, then ∠BOM=2x°;∠AOM=5x°.Angles BOM and AOM together form angle with the measure 210°, thus2x+5x=210,7x=210,x=30°and ∠BOM=60°, ∠AOM=150°.Consider isosceles triangle BOM. In this triangle,∠OBM=1/2(180°-60°)=60°.Consider isosceles triangle AOB. In this triangle,∠OAB=1/2(180°-150°)=15°.Consider isosceles triangle AOM. In this triangle,∠OAM=1/2(180°-150°)=15°.Thus, ∠BAM=15°+15°=30°