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Assertion (A) : $\triangle ABC \sim \triangle PQR$ such that $\angle A= 65^\circ, \angle C = 60^\circ$. Hence $\angle Q = 55^\circ$. Reason (R): Sum of all angles of a triangle is $180^\circ$
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 $\angle A= 65^\circ, \angle C = 60^\circ$. Hence $\angle Q = 55^\circ$.
Reason (R): Sum of all angles of a triangle is $180^\circ$
This Question has 1 answers.
### Given:
Assertion (A): $\triangle ABC \sim \triangle PQR$, and given angles:
$ \angle A = 65^\circ, \quad \angle C = 60^\circ $
We need to determine whether $\angle Q = 55^\circ$.
### Step 1: Find $\angle B$
Since the sum of the angles in a triangle is $180^\circ$:
$ \angle B = 180^\circ - (\angle A + \angle C) $
$ = 180^\circ - (65^\circ + 60^\circ) $
$ = 180^\circ - 125^\circ $
$ = 55^\circ $
### Step 2: Find $\angle Q$
Since $\triangle ABC \sim \triangle PQR$, their corresponding angles are equal:
$ \angle A = \angle P, \quad \angle B = \angle Q, \quad \angle C = \angle R $
Thus, $\angle Q = \angle B = 55^\circ$, which verifies the assertion.
### Step 3: Verify the Reason
The reason states that the sum of all angles in a triangle is $180^\circ$, which is a fundamental property of triangles.
### Conclusion:
### Final Answer: Assertion (A) is true, and Reason (R) is the correct explanation of (A).
Assertion (A): $\triangle ABC \sim \triangle PQR$, and given angles:
$ \angle A = 65^\circ, \quad \angle C = 60^\circ $
We need to determine whether $\angle Q = 55^\circ$.
### Step 1: Find $\angle B$
Since the sum of the angles in a triangle is $180^\circ$:
$ \angle B = 180^\circ - (\angle A + \angle C) $
$ = 180^\circ - (65^\circ + 60^\circ) $
$ = 180^\circ - 125^\circ $
$ = 55^\circ $
### Step 2: Find $\angle Q$
Since $\triangle ABC \sim \triangle PQR$, their corresponding angles are equal:
$ \angle A = \angle P, \quad \angle B = \angle Q, \quad \angle C = \angle R $
Thus, $\angle Q = \angle B = 55^\circ$, which verifies the assertion.
### Step 3: Verify the Reason
The reason states that the sum of all angles in a triangle is $180^\circ$, which is a fundamental property of triangles.
### Conclusion:
- Assertion (A) is true.
- Reason (R) is true.
- Reason (R) correctly explains Assertion (A).
### Final Answer: Assertion (A) is true, and Reason (R) is the correct explanation of (A).
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