Question

Assertion : If two internal opposite angles of a triangle are equal and external angle is given to be $110°$, then each of the equal internal angle is ${55}^{\circ }$
Reason : A triangle with one of its angle $90°$, is called a right triangle.
Which of the following is correct.

• A. If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
• B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.
• C. If Assertion is correct but Reason is incorrect.
• D. If Assertion is incorrect but Reason is correct.

Answer 1

The correct option is B

If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion.

Explanation of assertion:

If two interior opposite angles of a triangle are equal and the external angle is given to be $110°$, then each of the equal interior angle is $55°$
The external angle of a triangle $=$sum of opposite interior angles.
It is given that two interior opposite angles of a triangle are equal,

Let, each of the interior opposite angles
$\Rightarrow 110°=x+x$

$\Rightarrow 110°=2x$
$\Rightarrow 55°=x$

An exterior angle of a triangle is equal to the sum of the interior opposite angle here ${55}^{\circ }+{55}^{\circ }={110}^{\circ }$

Explanation of reason:

A triangle with one of its angle $90°$, is called a right angle triangle

Assertion and Reason both are correct but the reason is not an explanation of the assertion.

Hence, option (B) is the correct answer.