Question
Download Solution PDFThe sides AB and AC of AABC are produced D and E, respectively. The bisectors of ∠CBD and ∠BCE meet at P. If ∠P = 54° find the measure of ∠A.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
∠P = 54º
Sides AB and AC of ΔABC are produced to D and E, respectively.
The bisectors of ∠CBD and ∠BCE meet at P.
Formula Used:
Exterior Angle Property: ∠P = ∠CBD + ∠BCE
Sum of angles in a triangle: ∠A + ∠B + ∠C = 180º
Calculation:
Using the exterior angle property:
∠P = ∠CBD + ∠BCE
⇒ 54º = ∠B + ∠C
Using the sum of angles in a triangle:
∠A + ∠B + ∠C = 180º
⇒ ∠A + 54º = 180º
⇒ ∠A = 180º - 54º
⇒ ∠A = 72º
The measure of ∠A is 72º.
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