In an isosceles triangle- one angle is 70- The other two angles are ofi 55- and 55-ii 70- and 40-iii 55- and 40-In the given options which of the above statements are true-a i onlyb ii onlyc iii only d i and ii

The correct option is (d). It is given that one of the base angles of an isosceles triangle is 70^∘. We know that in an isosceles triangle, the 2 base angles a ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VII

Mathematics

Properties of Isosceles and Equilateral Triangles

In an isoscel...

Question

In an isosceles triangle, one angle is $70^{\circ}$ . The other two angles are of
(i) $55^{\circ}$ and $55^{\circ}$
(ii) $70^{\circ}$ and $40^{\circ}$
(iii) $55^{\circ}$ and $40^{\circ}$
In the given option(s) which of the above statement(s) are true?
(a) (i) only
(b) (ii) only
(c) (iii) only
(d) (i) and (ii)

Open in App

Solution

The correct option is (d).

It is given that one of the base angles of an isosceles triangle is $70^{\circ}$ .
We know that in an isosceles triangle, the $2$ base angles are equal.

Case 1: If $70^{\circ}$ is NOT the base angle, then the other two angles are base angles. Therefore, the base angles are of measure:

$70^{\circ} + x + x = 180^{\circ}$
$2 x + 70^{\circ} = 180^{\circ}$
$2 x = 180^{\circ} - 70^{\circ}$
$x = \frac{110^{\circ}}{2}$
$x = 55^{\circ}$
So, both the base angles are $55^{\circ}$ in measure.

Case 2: If $70^{\circ}$ is one of the base angles.
Then the other base angle would also measure $70^{\circ}$ ,
$70^{\circ} + 70^{\circ} + x = 180^{\circ}$
$x = 180^{\circ} - 140^{\circ}$
$x = 40^{\circ}$
So, one angle is $40^{\circ}$ and the other two base angles are of $70^{\circ}$ .

Hence, both (i) and (ii) are true.
Therefore, option (d) is correct.

Suggest Corrections

Similar questions

Question 5

In an isosceles triangle, one angle is $70^{\circ}$ . The other two angles are of

i) $55^{\circ}$ and $55^{\circ}$
ii) $70^{\circ}$ and $40^{\circ}$
iii) Any measure

In the given option(s) which of the above statement(s) are true?

a) (i) only
b) (ii) only
c) (iii) only
d) (i) and (ii)

Question 6

In a triangle, one angle is of $90^{\circ}$ . Then,

i) The other two angles are $45^{\circ}$ each.
ii) In remaining two angles, one angle is $90^{\circ}$ and other is $45^{\circ}$
iii) Remaining two angles are complementary

In the given option(s) which is true?

a) (i) only
b) (ii) only
c) (iii) only
d) (i) and (ii)

Q. Three statements are given below:
I. In a || gm, the angle bisectors of two adjacent angles enclose a right angle.
II. The angle bisectors of a || gm form a rectangle.
III. The triangle formed by joining the mid-points of the sides of an isosceles triangle is not necessarily an isosceles triangle.
Which is true?
(a) I only
(b) II only
(c) I and II
(d) II and III

Q. For an isosceles right-angled triangle having each of equal sides 'a', we have
I.

Area = \frac{1}{2} a^{2}

II.

Perimeter = (2 + \sqrt{2}) a

III. Hypotenuse = 2a
Which of the following is true?
(a) I only
(b) II only
(c) I and II
(d) I and III

Q. For an isosceles triangle having base b and each of the equal sides as a, we have:
I.

Area = \frac{b \cdot \sqrt{4 a^{2} - b^{2}}}{4}

II. Perimeter = (2a + b)
III.

Height = \frac{1}{2} \sqrt{4 a^{2} - b^{2}}

Which of the following is true?
(a) I only
(b) I and II only
(c) II and III only
(d) I, II and III

Join BYJU'S Learning Program

In an isosceles triangle, one angle is 70∘. The other two angles are of (i) 55∘ and 55∘ (ii) 70∘ and 40∘ (iii) 55∘ and 40∘ In the given option(s) which of the above statement(s) are true? (a) (i) only (b) (ii) only (c) (iii) only (d) (i) and (ii)