question_answer

Find the measures of the angles made by the intersecting lines at the vertices of an equilateral triangle.

Answer:

Let ABC be an equilateral triangle. Since, all the angles of an equilateral triangle are equal. \[\therefore \]\[\angle A\text{ }=\text{ }\angle B\text{ }=\text{ }\angle C\text{ }=\text{ }x{}^\circ \]      (say) We know that, sum of all the angles of a triangle is 180°. \[\angle A\text{ }+\text{ }\angle B\text{ }+\text{ }\angle C\text{ }=\text{ }180{}^\circ \] \[x{}^\circ \text{ }+\text{ }x{}^\circ \text{ }+\text{ }x{}^\circ \text{ }=\text{ }180{}^\circ \] \[3x{}^\circ \text{ }=\text{ }180{}^\circ \] \[x{}^\circ \text{ }=\text{ }60{}^\circ \] Hence,       \[\angle A\text{ }=\text{ }\angle B\text{ }=\text{ }\angle C\text{ }=\text{ 60}{}^\circ \]