Quadrilateral ABCD is inscribed in a circle.What is the measure of angle A?Enter your answer in the box.
Accepted Solution
A:
Answer:135°Step-by-step Explanation:==>Given:An inscribed quadrilateral ABCD with,m<A = (3x +6)°m<C = (x + 2)°==>Required:measure of angle A==>Solution:First, let's find the value of x. Recall that the opposite angles in any inscribed quadrilateral in a circle are supplementary.Therefore, this means m<A + m<C = 180°Thus, (3x+6) + (x+2} = 1803x + 6 + x + 2 = 180Collect like terms:3x + x + 6 + 2 = 1804x + 8 = 180Subtract 8 from both sides:4x + 8 - 8 = 180 - 84x = 172Divide both sides by 4:4x/4 = 172/4x = 43We can now find m<A = (3x + 6)°m<A = 3(43) + 6= 129 + 6measure of angle A = 135°