Assertion (A) : 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°.
Reason (R) : A triangle with one of its angle 90°, is called a right triangle.
[2 marks]

Both A and R are true, and R is the correct explanation for A.

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Both A and R are true, and R is not the correct explanation for A.

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A is true but R is false.

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A is false but R is true.

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Solution

The correct option is B Both A and R are true, and R is not the correct explanation for A.
The correct option is B.

Consider assertion (A) statement.
The external angle of a triangle = sum of opposite interior angles. It is given that two interior opposite angles of a triangle are equal.
[0.5 marks]

Let x be the measure of each of the interior opposite angles.
110° = x + x (by exterior angle property)
110° = 2x
55° = x
Consider reason (A) statement.
[0.5 marks]

A triangle with one of its angle 90°, is called a right triangle.
A and R both are correct, but the R is not an explanation of the A.
Hence, option (B) is the correct answer.
[1 mark]

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Similar questions

Q. An exterior angle of a triangle is 110° and its two interior opposite angles are equal. Each of these equal angles is
(a) 70°
(b) 55°
(c) 35°
(d) 27

\frac{1 °}{2}

Which of the following statements are true (T) and which are false (F):

(i) Sides opposite to equal angles of a triangle may be unequal.

(ii) Angles opposite to equal sides of a triangle are equal.

(iii) The measure of each angle of an equilateral triangle is 60°.

(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.

(v) The bisectors of two equal angles of a triangle are equal.

(vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.

(vii) The two altitudes corresponding to two equal sides of a triangle need not be equal.

(viii) If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent.

(ix) Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal equal to the hypotenuse and a side of the other triangle.

Q. Which of the following statements are true (T) and which are false (F):

(i) Sum of the three angles of a triangle is 180°.

(ii) A triangle can have two right angles.

(iii) All the angles of a triangle can be less than 60°

(iv) All the angles of a triangle can be greater than 60°.

(v) All the angles of a triangle can be equal to 60°.

(vi) A triangle can have two obtuse angles.

(vii) A triangle can have at most one obtuse angles.

(viii) If one angle of a triangle is obtuse, then it cannot be a right angled triangle.

(ix) If one angle of a triangle is obtuse, then it cannot be a right angled triangle.

(x) An exterior angle of a triangle is less than either of its interior opposite angles.

(xi) An exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Q. Assertion (A) : 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°.

Reason (R) : A triangle with one of its angle 90°, is called a right triangle.

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.

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Assertion (A) : 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°. Reason (R) : A triangle with one of its angle 90°, is called a right triangle. [2 marks]

Assertion (A) : 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°.
Reason (R) : A triangle with one of its angle 90°, is called a right triangle.
[2 marks]