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Maths-

General

Easy

Question

In the figure, ABCD is a kite with AB = AD, BC = CD and $stack A C with bar on top$ intersects $stack B D with bar on top$ at O. If $angle O A B equals 25 to the power of ring operator end exponent$ and $angle O D C equals 50 to the power of ring operator end exponent$ then a – b + c – d + e – f =

50
55
60
65

hint Hint:

Find the values of all unknown angles by using sum of angles in triangle is 180 degree , angles opposite to equal sides are equal and perpendicular drawn in a isosceles triangles from common vertex of equal sides divides the angle at vertex into two equal parts. Find the value of equation by substituting them.

The correct answer is: 55

AB = AD then a = c (angles opposite to equal sides are equal )
BC = CD then b = 50° (angles opposite to equal sides are equal )
perpendicular drawn in a isosceles triangles from common vertex of equal sides divides the angle at vertex into two equal parts.
Then, d = 25 and e = f
sum of angles in triangle is 180 degree then in triangle OAB
90 +25 +a = 180 °
a = 180°-115° = 65° then a = c =65°
Then, a – b + c – d + e – f = 65 - 50 + 65 - 25 + e - e = 15 + 40 + 0 = 55°
Therefore, a – b + c – d + e – f = 55°

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