Question

modeling with mathematics. using tools the sum of the angle measures of a quadrilateral is 360°. in exercises 17 - 20, write and solve an equation to find the value of x. use a protractor to check the reasonableness of your answer. 17. 100 120 100 x. 18. 150 77 48 x. 19. 76 92 122 x. 20. 115 85 60 x.

Explanation:

Step1: Recall angle - sum property

The sum of interior angles of a quadrilateral is $360^{\circ}$.

Step2: For Exercise 17

Set up the equation $100 + 120+100 + x=360$.
Combine like - terms: $320 + x=360$.
Subtract 320 from both sides: $x = 360-320=40$.

Step3: For Exercise 18

Set up the equation $150 + 77+48 + x=360$.
Combine like - terms: $275 + x=360$.
Subtract 275 from both sides: $x=360 - 275 = 85$.

Step4: For Exercise 19

Set up the equation $76+92 + 122+x=360$.
Combine like - terms: $290+x=360$.
Subtract 290 from both sides: $x=360 - 290=70$.

Step5: For Exercise 20

Set up the equation $115+85 + 60+x=360$.
Combine like - terms: $260+x=360$.
Subtract 260 from both sides: $x=360 - 260 = 100$.

Answer:

1. $x = 40^{\circ}$
2. $x = 85^{\circ}$
3. $x = 70^{\circ}$
4. $x = 100^{\circ}$