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# The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32º and ∠AOB = 70º, then ∠DBC is equal to

a. 24º

b. 86º

c. 38º

d. 32º

**Solution:**

Given,

ABCD is a parallelogram

AC and BD are the diagonals

AD || BC

∠DAC = ∠ACB [Alternate angle]

∠ACB = 32º

We know that

∠AOB + ∠BOC = 180º [Straight line]

Substituting the values

70º + ∠BOC = 180º

∠BOC = 110º

In Δ BOC,

∠OBC + ∠BOC + ∠OCB = 180º

Substituting the values

∠OBC + 110º + 32º = 180º

∠OBC = 38º

∠DBC = 38º

Therefore, ∠DBC is equal to 38º.

**✦ Try This: **The diagonals PR and QS of a parallelogram PQRS intersect each other at the point O. If ∠SPR = 50º and ∠POQ = 80º, then ∠SQR is equal to a. 24º, b. 86º, c. 38º, d. 32º

**☛ Also Check:** NCERT Solutions for Class 9 Maths Chapter 8

**NCERT Exemplar Class 9 Maths Exercise 8.1 Problem 12**

## The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32º and ∠AOB = 70º, then ∠DBC is equal to , a. 24º, b. 86º, c. 38º, d. 32º

**Summary:**

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32º and ∠AOB = 70º, then ∠DBC is equal to 38º

**☛ Related Questions:**

- If APB and CQD are two parallel lines, then the bisectors of the angles APQ, BPQ, CQP and PQD form , . . . .
- The figure obtained by joining the mid-points of the sides of a rhombus, taken in order, is ,a. a rh . . . .
- D and E are the mid-points of the sides AB and AC of ∆ABC and O is any point on side BC. O is joined . . . .

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