Question

Assertion: In the figure ∠ABC = 150°, ∠C = 35°, ∠ADE = 115°. ∴ ∠A = 60°.

Reason: Sum of the angles of a quadrilateral is 360°.

Options

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

A is false but R is true.

Explanation:

Assertion (A):

This problem involves finding an angle within a quadrilateral where one of the given angles is an exterior angle ∠ADE.

First, we need to find the interior angle ∠ADC. An interior angle and its corresponding exterior angle are supplementary, meaning they add up to 180°.

So, ∠ADC = 180° – ∠ADE = 180° – 115° = 65°.

Now we have three interior angles of the quadrilateral ABCD:

∠ABC = 150°, ∠C = 35° and ∠ADC = 65°.

The sum of the interior angles of a quadrilateral is 360°.

Therefore, ∠A = 360° – (∠ABC + ∠C + ∠ADC)

∠A = 360° – (150° + 35° + 65°)

∠A = 360° – (250°)

∠A = 110°

The assertion states that ∠A = 60°, which contradicts our calculated value of 110.

Therefore, the Assertion is false.

Reason (R):

This is a fundamental property of all quadrilaterals four-sided polygons. The sum of their interior angles is always 360°.

Therefore, the Reason is true.