Question

The angles of a quadrilateral have measures m∠A = (7x)◦, m∠B = (4x + 5)◦, m∠C =
(6x + 15)◦, m∠D = (6x −5)◦. Find the value of x. If a diagonal bisects ∠B and ∠D, what
type of quadrilateral is ABCD?

Answer 1

The value of x is 15° and the type of quadrilateral is a rhombus.

Quadrilateral

• A quadrilateral is a polygon that has four sides.

• The sum of all angles of a quadrilateral is 360°.

Here, we are given,

m∠A = (7x)◦, m∠B = (4x + 5)◦, m∠C =(6x + 15)◦, m∠D = (6x −5)◦

So, we will have

7x+4x+5+6x+15+6x-5=360°

23x+15°=360°

23x=345°

x=345°/23°

x=15°

Hence, the angles of the quadrilateral are:

m∠A = (7x)◦=105°,

m∠B = (4x + 5)◦ =65°

m∠C =105°

m∠D = (6x −5)◦ =85°

Since the diagonal bisects ∠B and ∠D, we get that the quadrilateral is a rhombus.

To learn more about rhombus refer to:

https://brainly.com/question/27870968

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