Question

If the degree measures of the angles of quadrilateral are 4x, 7x, 9x and 10x, what is the sum of the measures of the smallest angle and largest angle?

Options

• 140°

• 150°

• 168°

•  180°

Answer 1

We have,

∠A = 4x,

∠B = 7x,

∠C = 9x,

and ∠D = 10x,

By angle sum property of a quadrilateral, we get:

∠A +∠B + ∠C + ∠D = 360

    4x + 7x + 9x 10x = 360

                         30x = 360

                            `x = (360)/30`

                             x = 12 

Smallest angle:

∠A = 4x

∠A = 48°

Also, Largest angle:

∠D = 10x

∠D = 10(12°)

∠D = 120°

Thus, the sum of the smallest and the largest becomes:

∠A +∠D = 48° + 120°

∠A + ∠D = 168°

Hence, the correct choice is (c).