Question

a diagonal is drawn on a square. how many triangles are formed? what is the sum of the measures of the angles of a triangle? what is the sum of the angle measures of the square?

Explanation:

Step1: Count the number of triangles

When a diagonal is drawn in a square, \(2\) triangles are formed.

Step2: Recall the angle - sum property of a triangle

By the angle - sum property of a triangle, the sum of the measures of the angles of a triangle is \(180^{\circ}\).

Step3: Calculate the sum of the angle measures of the square

Since the square is divided into \(2\) triangles by the diagonal, and the sum of angles of each triangle is \(180^{\circ}\), the sum of the angle measures of the square is \(2\times180^{\circ}=360^{\circ}\)

Answer:

\(2\)
\(180^{\circ}\)
\(360^{\circ}\)