Question

An exterior angle of a triangle is 100 degree and it’s interior opposite angles are equal to each other. Find the measure of each angle of the triangle.

Answer 1

Answer:

180 degrees

because sum of all sides of a triangle is 180

I don't know what I am telling I am in grade 5 lol

Answer 2

Step-by-step explanation:

Using the theorem that if the side of a triangle is produced then the interior angle is equal to the sum of two interior opposite angles of the triangle.Let $\bf\Delta ABC$ be a triangle where the side BC is produced. By the theorem we have

$\tt \angle A +\angle B =100^{\circ} \ldots \ldots \ldots \ldots (1)$

It is given that the interior opposite angles are equal i.e., $\bf \angle A =\angle B$

$\text{ \( \therefore \) Equation (1) becomes}$

$\pmb{ \[ \begin{array}{l} \tt 2 \angle A =100^{\circ} \\ \tt \Rightarrow \angle A =50^{\circ} \\ \tt \Rightarrow \angle B =50^{\circ} \end{array} \]}$

Using angle sum property of a triangle, Sum of all angles of a triangle =180°

$\pmb{\[ \begin{array}{l} \tt \Rightarrow \angle A +\angle B +\angle C =180^{\circ} \\ \tt \Rightarrow 100+\angle C =180^{\circ} \text { [from (1)] } \\ \tt \Rightarrow \angle C =180^{\circ}-100^{\circ} \\ \tt \Rightarrow \angle C =80^{\circ} . \end{array} \]}$

$\pmb{ \[ \begin{array}{l} \tt\text { Hence } \angle A =50^{\circ} \\ \tt\angle B =50^{\circ} \\ \tt \angle C =80^{\circ} . \end{array} \]}$