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(1) Seg AB is the diameter of a circle. C is the point on the circumference such that in△ABC, LB is less by 10° than LA. Find the measures of all angles of △ABC.2) The measurements (in mm) of the diameters of the heads of the screws are givenbelow. Calculate the mean diameter of the head of the screws.Diameter (in mm) 33-35 36-38 39-4 42-44r of serews (.)17 1923 21 |
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Answer» Let the measures of ∠A be xº and measure of ∠B be yº. Seg AB is the diameter of a circle and C is a point on the circumference. ∴ m ∠C = 900[∵ The angle subtended by a diameter at any point on the circle other than its end points is a right angle] In ∆ ABC,m ∠A + m ∠B + m ∠C = 1800[∵ Sum of measures of the angles of a triangle is 1800]∴ x + y + 90 = 180∴ x + y = 180 – 90∴ x + y = 90 ........eq. no. (1)As the given condition,∠ B = ∠ A – 100∴ y = x - 10∴ x – y = 10 ......... eq. no. (2)Adding equations (1) and (2)x + y = 90x – y = 102x = 100∴ x = 100/2∴ x = 50Substituting x = 50 in equation no. (1)x + y = 90∴ 50 + y = 90∴ y = 90 – 50∴ y = 40The measures of angle of ∆ ABC are 50º, 40º and 90º. |
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