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Mathematics

Assertion (A): Using the information in the given figure, we get x = 40°.

Using the information in the given figure, we get x = 40°. Assertion Reasoning, Concise Mathematics Solutions ICSE Class 9.

Reason (R):

Using the information in the given figure, we get x = 40°. Assertion Reasoning, Concise Mathematics Solutions ICSE Class 9.

⇒ x + (x + 40°) + 40° = 180°
x = 50°

  1. A is true, R is false.
  2. A is false, R is true.
  3. Both A and R are true.
  4. Both A and R are false.

Triangles

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Answer

A is false, R is true.

Explanation

In Δ ADC,

∠ DAC = ∠ DCA (Opposite angles of equal sides are always equal)

∴ ∠ DAC = 40 °

Sum of all angles of triangle is 180°.

∠ DAC + ∠ DCA + ∠ ADC = 180°

⇒ 40° + 40° + ∠ ADC = 180°

⇒ 80° + ∠ ADC = 180°

⇒ ∠ ADC = 180° - 80°

⇒ ∠ ADC = 100°

Now, ∠ ADC and ∠ ADB forms a linear pair.

So, ∠ ADC + ∠ ADB = 180°

⇒ 100° + ∠ ADB = 180°

⇒ ∠ ADB = 180° - 100°

⇒ ∠ ADB = 80°

In Δ ABD,

∠ ABD = ∠ DAB (Opposite angles of equal sides are always equal)

∴ ∠ DAB = x°

Sum of all angles of triangle is 180°.

∠ ABD + ∠ ADB + ∠ DAB = 180°

⇒ x° + 80° + x° = 180°

⇒ 2x° + 80° = 180°

⇒ 2x° = 180° - 80°

⇒ 2x° = 100°

⇒ x° = 100°2\dfrac{100°}{2}

⇒ x° = 50°

∴ Assertion (A) is false.

⇒ x + (x + 40°) + 40° = 180°

⇒ x + x + 40° + 40° = 180°

⇒ 2x + 80° = 180°

⇒ 2x = 180° - 80°

⇒ 2x = 100°

⇒ x = 100°2\dfrac{100°}{2}

⇒ x = 50°

∴ Reason (R) is true.

Hence, Assertion (A) is false, Reason (R) is true.

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