Question

Take any quadrilateral, say ABCD. Divide it into two triangles by drawing a diagonal. You get six angles: 1, 2, 3, 4, 5, and 6. Use the angle sum property of a triangle and argue how the sum of the measures of angle A, angle B, angle C, and angle D amounts to 180° + 180° = 360°.

a) True
b) False

Answer 1

When a quadrilateral is divided into two triangles by drawing a diagonal, the sum of the measures of the angles in the quadrilateral is 360°.

Step-by-step explanation:

When a quadrilateral is divided into two triangles by drawing a diagonal, we can use the angle sum property of a triangle to argue that the sum of the measures of angle A, angle B, angle C, and angle D amounts to 180° + 180° = 360°. This is because each triangle has angles that add up to 180°, and since there are two triangles, the total sum is 180° + 180° = 360°.