# ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is

a. 40º

b. 45º

c. 50º

d. 60º

**Solution:**

From the question

ABCD is a rhombus

∠ACB = 40º

From the figure

∠ACB = 40°

∠OCB = 40°

As AD ∥ BC

∠DAC = ∠BCA = 40° (Alternate interior angles)

∠DAO = 40°

Diagonals of a rhombus are perpendicular to each other

∠AOD = 90°

From the angle sum property of triangle, the sum of interior angles of a triangle is 180°

We can write it as

∠AOD + ∠ADO + ∠DAO = 180°

Substituting the values

90° + ∠ADO + 40° = 180°

130° + ∠ADO = 180°

So we get

∠ADO = 180° – 130°

∠ADO = 50°

∠ADB = 50°

Therefore, ∠ADB is 50°.

**✦ Try This: **PQRS is a rhombus such that ∠PRQ = 50º. Then ∠PSQ is a. 40º, b. 45º, c. 50º, d. 60º

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

**NCERT Exemplar Class 9 Maths Exercise 8.1 Problem 3**

## ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is , a. 40º, b. 45º, c. 50º, d. 60º

**Summary:**

ABCD is a rhombus such that ∠ACB = 40º. Then ∠ADB is 50°

**☛ Related Questions:**

- The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in or . . . .
- The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in or . . . .
- If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4, then AB . . . .

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