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ABCD is a parallelogram with ∠A= 80°. The internal bisectors ∠B and ∠C meet at O. Find the measure of three angles of triangle BCO

Answer» <html><body><p><strong>Step-by-step <a href="https://interviewquestions.tuteehub.com/tag/explanation-455162" style="font-weight:bold;" target="_blank" title="Click to know more about EXPLANATION">EXPLANATION</a>:</strong></p><p>∠A = 80°</p><p>We know that the opposite <a href="https://interviewquestions.tuteehub.com/tag/angles-378243" style="font-weight:bold;" target="_blank" title="Click to know more about ANGLES">ANGLES</a> of a parallelogram are equal.</p><p>∠A = ∠C = 80°</p><p>And</p><p>∠OCB = (1/2) × ∠C</p><p>= (1/2) × 80°</p><p>= 40°</p><p>∠B = 180° – ∠A (the sum of interior angles on the same side of the <a href="https://interviewquestions.tuteehub.com/tag/transversal-1426600" style="font-weight:bold;" target="_blank" title="Click to know more about TRANSVERSAL">TRANSVERSAL</a> is 180)</p><p>= 180° – 80°</p><p>= 100°</p><p>Also,</p><p>∠CBO = (1/2) × ∠B</p><p>= (1/2) × 100°</p><p>= 50°</p><p>By the angle sum property of <a href="https://interviewquestions.tuteehub.com/tag/triangle-1427233" style="font-weight:bold;" target="_blank" title="Click to know more about TRIANGLE">TRIANGLE</a> BCO,</p><p>∠BOC + ∠OBC + ∠CBO = 180°</p><p>∠BOC = 180° – (∠OBC + CBO)</p><p>= 180° – (40° + 50°)</p><p>= 180° – 90°</p><p>= 90°</p><p>Hence, the measure of all the three angles of a triangle BCO is 40°, 50° and 90°.</p><p></p></body></html>


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