Question

4. ABCD is a rhombus. The
measure of angle OAB = 30°.
Calculate (i) angle OBA (ii) angle DAB (iii) angle BCD
(iv) angle ABC​

Answer 1

Answer:

(i)angle OBA = 60

(ii) angle DAB = 60

(iii) angle BCD = 60

(iv) angle ABC​ = 120

Explanation:

Given: angle OAB = 30

To find: (i) angle OBA (ii) angle DAB (iii) angle BCD

(iv) angle ABC​

Solution: angle DAB = 30 + 30 = 60(Angle bisector)

angle BCD = angle DAB = 60 (opposite angles in a rhombus are equal)

angle DAB + angle BCD + angle ADC + angle ABC = 360(Rhombus is a quadrilateral)

60 + 60 + angle ADC + angle ABC = 360(angle DAB = angle BCD = 60)

2(angle ABC) = 360 - 120(angle ADC = angle ABC as opposite angles are equal)

angle ABC = 240/2

angle ABC = 120

angle OBA = 1/2 x angle ABC(angle bisector)

                  = 1/2 x 120

                  = 60