9. Assertion: The angles of a triangle are in the ratio 2:3:4. The largest angle of the triangle is 80°. Reason: The sum of all the interior angles of a triangle is 180° Ans: We know that the sum of all the interior angles of a triangle is 180º. So, Reason (R) is true. Let the angles of a triangle be 2x, 3x and 4x then we have 2x + 3x + 4x = 180° 9x = 180° x = 20° Hence, Largest angle = 4 x 20° = 80°. So, Assertion (A) is also true. Also, Reason (R) is a correct explanation of Assertion (A). Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
why we have took 4 to multiply with 20°
Answers
Answer:
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Step-by-step explanation:
are true and reason is the correct explanation of assertion
Both Assertion (A) and Reason (R) is correct and R is the correct explanation of A.
Given: The angles of a triangle are in the ratio 2:3:4.
To find: Largest angle of the triangle
Solution: The angles of the triangle are in the ratio 2:3:4. Therefore, let the angles be 2x, 3x and 4x respectively.
"According to the angle sum property of the triangle, the sum of the measures of the interior angles of a triangle is 180°."
Therefore, the sum of 2x, 3x and 4x should also be equal to 180°.
2x + 3x + 4x = 180°
=> 9x = 180°
=> x = 180/9
=> x = 20°
Since x = 20°, the measure of other angles are as follows:
2x = 2 × 20° = 40°
3x = 3 × 20° = 60°
4x = 4 × 20° = 80°
Clearly, the largest angle among them is 80° which implies that the assertion was correct and the angle sum property given as the reason is the apt theory for solving the question.