Question

In the given rhombus ABCD,diagonals intersect at O .If angle ABO = 53degree .find

A)OAB
B)ADC
C)BCD

Answer 1

Use sum of all angles is 180 degree

Answer 2

Given,

ABCD is a rhombus

Diagonals AC and DB intersect at O

∠ABO = 53°

To find,

a) OAB

b) ADC

c) BCD

Solution,

As we know that ABCD is a rhombus and rhombus diagonals intersect each at 90° therefore,

∠AOB = ∠AOD = ∠DOC = ∠COB = 90°

∆AOB is a right angle triangle and according to right angle triangle theory, the Sum of all angles of the Triangle is 180°. Therefore,

∠OAB = 180°- (∠AOB+∠ABO)

= 180° - (90°+53°)

∠OAB = 37°

∠OAB = ∠OCD = 37° (Alternative angles)

Similarly,

∠ABO = ∠ODC (Alternative angles)

∠ADB = ∠ABD (Alternative angles)

Another property of the rhombus is the hat diagonals of the rhombus divides an angle into equal two halves. Therefore,

∠ADB =∠ABD =∠DBC =∠ODC = 53°

Similarly,

∠OAB =∠OCD =∠OAD =∠OCB = 37°

Hence,

a) ∠OAB = 37°

b)∠ADC = ∠ADO+ ∠ODC = 53°+53° = 106°

c) ∠BCD = ∠BCO+ ∠OCD = 37°+37° = 74°