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Assertion (A): $\triangle ABC \sim \triangle PQR$ such that $\angle A = 65^\circ, \angle C = 55^\circ$. Reason (R): Sum of all angles of a triangle is 180°.
Directions : In question below a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option :
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not correct explanation for Assertion (A).
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false, but Reason (R) is true.
Assertion (A): $\triangle ABC \sim \triangle PQR$ such that $\angle A = 65^\circ, \angle C = 55^\circ$.
Reason (R): Sum of all angles of a triangle is 180°.
This Question has 1 answers.
Sum of angles in $\triangle ABC$:
$\angle A + \angle B + \angle C = 180^\circ$
Substituting given values:
$65^\circ + \angle B + 55^\circ = 180^\circ$
$\angle B = 180^\circ - 120^\circ = 60^\circ$
Since $\triangle ABC \sim \triangle PQR$, their corresponding angles are equal:
$\angle A = \angle P = 65^\circ$,
$\angle B = \angle Q = 60^\circ$,
$\angle C = \angle R = 55^\circ$.
Thus, Assertion (A) is true.
Reason (R) states that the sum of angles in a triangle is $180^\circ$, which is a true mathematical fact.
$\angle A + \angle B + \angle C = 180^\circ$
Substituting given values:
$65^\circ + \angle B + 55^\circ = 180^\circ$
$\angle B = 180^\circ - 120^\circ = 60^\circ$
Since $\triangle ABC \sim \triangle PQR$, their corresponding angles are equal:
$\angle A = \angle P = 65^\circ$,
$\angle B = \angle Q = 60^\circ$,
$\angle C = \angle R = 55^\circ$.
Thus, Assertion (A) is true.
Reason (R) states that the sum of angles in a triangle is $180^\circ$, which is a true mathematical fact.
However, it is not specifically explaining why $\triangle ABC \sim \triangle PQR$.
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation for Assertion (A).
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation for Assertion (A).
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