Question

If the angles of a triangle are in the ratio 1:2:7 then the triangle is
a) Right angled b) Isosceles
c) Obtuse angled d)acute angled​

Answer 1

Answer :-

• Option c is correct.
• It is an obtuse angled triangle.

Given :-

• The angles of a triangle are in the ratio 1 : 2 : 7.

To find :-

• Whether the triangle is right angled, isoceles, obtuse angled or acute angled.

Step-by-step explanation :-

• Before finding what type of triangle it is, we have to find all the angles of the triangle.

• The angles of a triangle are in the ratio 1 : 2 : 7, so let the angles be x, 2x and 7x respectively.

We know that :-

$\underline{ \boxed{ \sf Sum \: of \: all \: angles \: in \: a \: triangle = 180^{\circ}}}$

----------------

$\sf \longmapsto x + 2x + 7x = 180^{\circ}$

Adding x, 2x and 7x,

$\sf \longmapsto 10x = 180^{\circ}$

Transposing 10 from LHS to RHS, changing it's sign,

$\sf\longmapsto x = \dfrac{ \: 180^{\circ}}{10}$

Dividing 180° by 10,

$\longmapsto \overline{\boxed{ \sf x = 18^{\circ}}}$

----------------

Hence, all the angles are as follows :-

$\bf x = 18^{ \circ}$

$\bf2x = 2 \times 18^{ \circ} = 36^{ \circ}$

$\bf7x = 7 \times 18^{ \circ} = 126^{ \circ}$

----------------

We observe that :-

• In this triangle, one of the angles is more than 90°.

• Hence, it is an obtuse angled triangle.

• So, option c is correct.