Answer:
142°
Step-by-step explanation:
Sum of interior angles of a polygon= (n -2) ×180°, where n is the number of sides of the polygon
Since this polygon has 5 sides, n= 5.
Sum of interior angles
= (5 -2) ×180°
= 3 ×180°
= 540°
Sum of interior angles= 540°
5x +8+5x +10 +6x +15 +7x +2 +2x +5= 540
Grouping like terms together:
5x +5x +6x +7x +2x +8 +10 +15 +2 +5= 540
Simplify:
25x +40= 540
Bringing all constants to one side of the equation:
25x= 540 -40
25x= 500
Divide both sides by 25:
x= 500 ÷25
x= 20
The angle (7x +2)° is the largest interior angle in this polygon.
7x +2
= 7(20) +2
= 142
Thus, the largest interior angle is 142°.
Check:
5x +8= 5(20) +8= 108
5x +10= 5(20) +10= 110
6x +15= 6(20) +15= 135
2x +5= 2(20) +5= 45
The other interior angles are 108°, 110°, 135° and 45°. Hence 142° is the largest interior angle in this polygon.
