Question

Assertion: Two angles measures a – 60° and 123° – 2a. If each one is opposite to equal sides of an isosceles triangle, then the value of a is 61°. Reason: Sides opposite to equal angles of a triangle are equal. *

-Both assertion (A) and reason (R) are true but (R) is the correct explanation of (A).
-Both assertion (A) and reason (R) are true but (R) is not the correct explanation of (A).
-Assertion (A) is true but reason (R) is false.
-Assertion (A) is false but reason (R) is true


which option is correct????

Answer 1

Answer:

Both assertion (A) and reason (R) are true but (R) is not the correct explanation of (A).

Answer 2

Given: Two angles measures $\[\left( {a-60^\circ } \right)and{\rm{ }}\left( {123^\circ -2a} \right)\]$ respectively.

Check whether the value of $a$ is $\[{61^ \circ }\]$.

Understand that, the sides opposite to equal angles of a triangle are equal.

Therefore,

$\[\begin{array}{l}\left( {a - {{60}^ \circ }} \right) = \left( {{{123}^ \circ } - 2a} \right)\\ \Rightarrow 2a + a = {123^ \circ } + {60^ \circ }\\ \Rightarrow 3a = 183\end{array}\]$

$\[\begin{array}{l} \Rightarrow a = \frac{{183}}{3}\\ \Rightarrow a = {61^ \circ }\end{array}\]$

Therefore, the given assertion(A) is true and the Reason (R) is true and the (R) is the correct explanation of (A).

Hence, the correct answer is option (a).