Question

solve for x.
17)

55° x + 74

54°

18)

8x + 2

70° 60°

19)

64°

27°

97 + x

20)

x + 51

80° 60°

Explanation:

Step1: 17) Use the triangle - angle sum property

The sum of angles in a triangle is \(180^{\circ}\). So, \(55^{\circ}+54^{\circ}+(x + 74)^{\circ}=180^{\circ}\).
First, simplify the left - hand side: \(55+54+x + 74=180\).
Combine like terms: \(x+(55 + 54+74)=180\), \(x + 183=180\).
Subtract 183 from both sides: \(x=180 - 183=-3\).

Step2: 18) Use the triangle - angle sum property

The sum of angles in a triangle is \(180^{\circ}\). So, \((8x + 2)^{\circ}+70^{\circ}+60^{\circ}=180^{\circ}\).
Simplify the left - hand side: \(8x+2+70 + 60=180\), \(8x+132=180\).
Subtract 132 from both sides: \(8x=180 - 132 = 48\).
Divide both sides by 8: \(x=\frac{48}{8}=6\).

Step3: 19) Use the exterior - angle property

The exterior - angle property states that the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(97 + x=64+27\).
Simplify the right - hand side: \(97+x=91\).
Subtract 97 from both sides: \(x=91 - 97=-6\).

Step4: 20) Use the exterior - angle property

First, find the non - labeled angle adjacent to \(x + 51\). The sum of angles on a straight line is \(180^{\circ}\). The non - labeled angle adjacent to \(x + 51\) is \(180-(80 + 60)=40^{\circ}\).
Then, using the triangle - angle sum property (or exterior - angle property in another way), \(x + 51=80+60\).
Simplify the right - hand side: \(x+51 = 140\).
Subtract 51 from both sides: \(x=140 - 51=89\).

Answer:

1. \(x=-3\)
2. \(x = 6\)
3. \(x=-6\)
4. \(x = 89\)