A park in the shape of quadrilateral PQRS is bordered by four sidewalks. Find the measure of each
1 answer:
Answer:
135°, 63°, 63°, 99°
Step-by-step explanation:
Find attached the diagram used in solving the question.
We would use formula for sum of interior angles to get each exterior angle.
From the diagram, we added additional variables to be able to solve for sum of interior angles.
Sum of angle on a straight line = 180°
a° +15z° = 180°
b° +7z° = 180°
c° +7z° = 180°
d° +11z° = 180°
Where a,b,c and d are interior angles
Sum of interior angles = 180(n-2)
n = number of sides
For quadrilateral, n= 4
a°+b°+c°+d° = 180(n-2)
180-15z +180-7z+180-7z+180-11z = 180(4-2)
720-40z = 180(2)
720 - 360 = 40z
z = 360/40
z = 9
Each exterior angle:
15z = 15×9 = 135°
7z = 7×9 = 63°
7z = 7×9 = 63°
11z = 11×9 = 99°
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