Question
Download Solution PDFIn a quadrilateral ABCD, ∠A = 86° and ∠B = 72°. The bisectors of ∠C and ∠D meet at O. What is the measure of ∠DOC?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
In quadrilateral ABCD, ∠A = 86° and ∠B = 72°
Bisectors of ∠C and ∠D meet at O.
Concept used:
In a quadrilateral, sum of all internal angles is 360°.
Bisectors intersect the angles at exactly half of their values.
Calculation:
Sum of all angles = ∠A + ∠B +∠C +∠D = 360°
∠C +∠D = 360°- 86°+ 72° = 202°
In ∆ DOC,
\({∠D \over 2} + ∠O +{∠C \over 2} = 180°\\ ∠O = 180° - {∠D + ∠C \over 2}\\ ∠O = 180° - {202 \over 2}\\ ∠O = 180° - 101° \\ ∠O = 79°\)
Therefore, ∠DOC is 79°.
Last updated on Jul 18, 2025
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