Answered

IDNLearn.com offers a unique blend of expert answers and community-driven knowledge. Get comprehensive answers to all your questions from our network of experienced experts.

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?

Sagot :

Answer:

see explanation

Step-by-step 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

Your participation is crucial to us. Keep sharing your knowledge and experiences. Let's create a learning environment that is both enjoyable and beneficial. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.