Question

In the given figure, if x°, yº and zº
are exterior angles of triangle ABC, then
find the value of xº + yº + zº.​

Answer 1

Given :

• x°, y° and z° are the exterior angles of a triangle ABC.

To Find :

• The value of x° + y° + z°

Solution :

As per the diagram, let's take,

$\dashrightarrow \: \: \bf \: x^{\circ} = \angle \: AB$

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$\dashrightarrow \: \: \bf \: y^{\circ} = \angle \: AC$

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$\dashrightarrow \: \: \bf \: z^{\circ} = \angle \: BC$

According to the Question,

Let's add x°, y° and z°.

As we know,

• $\underline{\boxed{ \sf{Sum \: of \: exterior \: angles_{(Triangle)} = 180^{\circ}}}}$

$\dashrightarrow \: \: \bf \: x^{\circ} + y^{\circ} + z^{\circ} = 2 \times 180^{\circ}$

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$\dashrightarrow \: \: \underline{ \boxed{\bf \:{ x^{\circ} + y^{\circ} + z^{\circ} = 360^{\circ}}}} \blue{ \bigstar}$

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$\therefore \: \underline{ \sf{The \: value \: of \: x^{\circ} + y^{\circ} + z^{\circ} = \bf{360^{\circ}}}}$