Question

The angles in a quadrilateral are 4y - 10°, y + 40°, 3y + 20° and 2y + 10° in order as you go around the quadrilateral.

a) Set up and solve an equation, to find the value of y.
b) Hence work out the value of each angle.
c) What type of quadrilateral is this?

Answer 1

see explanation

Explanation:

the sum of the interior angles of a quadrilateral = 360°

sum the 4 angles and equate to 360

4y - 10 + y + 40 + 3y + 20 + 2y + 10 = 360 , that is

10y + 60 = 360 ( subtract 60 from both sides )

10y = 300 ( divide both sides by 10 )

y = 30

then 4 angles are

4y - 10 = 4(30) - 10 = 120 - 10 = 110°

y + 40 = 30 + 40 = 70°

3y + 20 = 3(30) + 20 = 90 + 20 = 110°

2y + 10 = 2(30) + 10 = 60 + 10 = 70°

Since the angles measures are in order around the quadrilateral, then

the opposite angles are congruent, thus quadrilateral is a parallelogram