Question

One of the exterior angle of a triangle is 120 degree. The interior opposite angles are equal to eachother. Find the measure of all angles of the triangle. ​

Answer 1

Given :

• One of the Exterior angle of a triangle is 120°

• The interior opposite angles are equal

To Find :

• The measure of all angles of the Triangle

Concept used :

• Sum of two interior opposite angles of a triangle is equal to the exterior angle of the triangle. This is known as Exterior angle property

• Sum of all interior angles of a triangle is 180° . This property is known as Angle sum property

Figure :

$\setlength{\unitlength}{2mm}\begin{picture}(0,0)\thicklines \put(0,0){\vector(3,0){4cm}}\put(0,0){\line(3,4){1.5cm}}\put(15,0){\line(-3,4){1.5cm}}\qbezier(1.5,2)(3,2)(3,0)\put(3,2){\bf x}\qbezier(6,8)(7,6)(8.7,8)\put(7,5){\bf x}\qbezier(13.4,2)(16,3)(17,0)\put(16,2){\bf 120}\end{picture}$

Solution :

Let the two Interior angles of the triangle be x° , x°

Now using the Exterior angle property ,

$: \implies \sf\: x {}^{ \circ} + x {}^{ \circ} = 120 {}^{ \circ} \\ \\ : \implies \sf \: 2 {x}^{ \circ} = 120 {}^{ \circ} \\ \\ : \implies \sf x = \frac{120 {}^{ \circ} }{2} \\ \\ : \implies \sf \: x = {60}^{ \circ}$

So , The two interior opposite angles are 60° and 60°

Let the other angle be y°

Now ,

using angle sum property we get ,

$: \implies \sf \: 60 {}^{ \circ} + {60}^{ \circ} + y {}^{ \circ} = 180 {}^{ \circ} \\ \\ : \implies \sf \: {120}^{ \circ} + {y}^{ \circ} = {180}^{ \circ} \\ \\ : \implies \sf \: y = {180}^{ \circ} - {120}^{ \circ} \\ \\ \ : \implies \sf \: y = 60 {}^{ \circ}$

∴ The angles of the triangle are 60° , 60° and 60°

Answer 2

Answer:

Given :

One of the Exterior angle of a triangle is 120°

The interior opposite angles are equal

To Find :

The measure of all angles of the Triangle

Concept used :

Sum of two interior opposite angles of a triangle is equal to the exterior angle of the triangle. This is known as Exterior angle property

Sum of all interior angles of a triangle is 180° . This property is known as Angle sum property

Figure :

\setlength{\unitlength}{2mm}\begin{picture}(0,0)\thicklines \put(0,0){\vector(3,0){4cm}}\put(0,0){\line(3,4){1.5cm}}\put(15,0){\line(-3,4){1.5cm}}\qbezier(1.5,2)(3,2)(3,0)\put(3,2){\bf x}\qbezier(6,8)(7,6)(8.7,8)\put(7,5){\bf x}\qbezier(13.4,2)(16,3)(17,0)\put(16,2){\bf 120}\end{picture}

Solution :

Let the two Interior angles of the triangle be x° , x°

Now using the Exterior angle property ,

\begin{gathered} : \implies \sf\: x {}^{ \circ} + x {}^{ \circ} = 120 {}^{ \circ} \\ \\ : \implies \sf \: 2 {x}^{ \circ} = 120 {}^{ \circ} \\ \\ : \implies \sf x = \frac{120 {}^{ \circ} }{2} \\ \\ : \implies \sf \: x = {60}^{ \circ} \end{gathered}

:⟹x

∘

+x

∘

=120

∘

:⟹2x

∘

=120

∘

:⟹x=

2

120

∘

:⟹x=60

∘

So , The two interior opposite angles are 60° and 60°

Let the other angle be y°

Now ,

using angle sum property we get ,

\begin{gathered} : \implies \sf \: 60 {}^{ \circ} + {60}^{ \circ} + y {}^{ \circ} = 180 {}^{ \circ} \\ \\ : \implies \sf \: {120}^{ \circ} + {y}^{ \circ} = {180}^{ \circ} \\ \\ : \implies \sf \: y = {180}^{ \circ} - {120}^{ \circ} \\ \\ \ : \implies \sf \: y = 60 {}^{ \circ} \end{gathered}

:⟹60

∘

+60

∘

+y

∘

=180

∘

:⟹120

∘

+y

∘

=180

∘

:⟹y=180

∘

−120

∘

:⟹y=60

∘

∴ The angles of the triangle are 60° , 60° and 60°