There are five points A, B, C, D, and E on the circumference as shown in the figure below.
AB = BC, and DE = EA.
∠A = 105 degrees
∠C － ∠D = 25 degrees
Find the size of ∠C.
Answer
125 degrees
Solution
According to the statement of the problem, angles are shown in the figure below.
In this figure, as ∠A = 105 degrees, P + Q = 105 degrees and ∠C － ∠D = 25, (P+S) - (Q+S) = P - Q = 25 degrees.
Thus P = (105 + 25) / 2 = 65 degrees and Q = 40 degrees.
The sum total of the interior angle of the pentagon is 540 degrees.
2S = 540 - (P+Q) × 4 = 540 - 420 = 120
Thus S = 120/2 = 60 degrees.
∠C = P +S = 65 + 60 = 125 degrees.
