Question

I’m revising a test, can someone please help me?

Answer 1

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.