Question

The interior angles of a quadrilateral (2x+15), (2x-15), (3x+75), and (3x-25).
a) Find the value of x.
b) Find the smallest interior angle of the quadrilaterals.
c) Find the smallest exterior angle of the quadrilaterals.

Answer 1

Answer:

See the attachment.

Step-by-step explanation:

Answer 2

Step-by-step explanation:

We know that the sum of interior angles of quadrilateral is 360°.

So (2x+15)+(2x-15)+(3x+75)+(3x-25)=360°

a) 2x+15+2x-15+3x+75+3x-25=360°

10x+50=360

10x=360-50

10x=310

x=310/10

x=31

so, by applying the value for every interior angles

we get 2x+15

=2(31)+15

=62+15

=77°

2x-15

=2(31)-15

=62-15

=47°

3x+75

=3(31)+75

=93+75

=168

3x-25

=3(31)-25

=93-25

=68

b) The smallest interior angle is 47°. (2x-15)

we know that the exterior angle of a quadrilateral sum up 360°

so 360-77=283

360-47=313

360-168=192

360-68=292

c) The smallest exterior angle is 192°.