The value of x is 15° and the type of quadrilateral is a rhombus.
<h3>
Quadrilateral</h3>
- 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:
brainly.com/question/27870968
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