Question

Determine the value of each variable. Enter your answers as decimals. x = Blank #1 y = Blank #2 z = Blank #3 Question 1 options: Blank # 1 Blank # 2 Blank # 3

Answer 1

When two lines are Parallel

1.Corresponding Angles are equal.

2.Alternate interior angles are equal.

3. Sum of interior angle on the same side of transversal is 180°.

`1.(6x)/(5)+10^(\circ)+y^(\circ)=180^(\circ)\\\\y=170^(\circ)-(6x)/(5)\\\\2.y^(\circ)+z^(\circ)=180^(\circ)\\\\z^(\circ)=(2x-13)^(\circ)\\\\y^(\circ)+(2x-13)^(\circ)=180^(\circ)\\\\170^(\circ)-(6x)/(5)+(2x-13)^(\circ)=180^(\circ)\\\\ (4x)/(5)=10^(\circ)+13^(\circ)\\\\(4x)/(5)=23^(\circ)\\\\ x=(115)/(4){\circ}\\\\ x=28 (3)/(4)\\\\y=170^(\circ)-(6* 115)/(5 * 4)\\\\y=170^(\circ)-34.50^(\circ)\\\\y=135(1)/(2)^(\circ)\\\\z=180^(\circ)-y^(\circ)`

z=180°-(135.50)°

z=(44.50)°

`z=44(1)/(2)^(\circ)`

Answer 2

x=31.25°

y=49.5°

z=130.5°

Explanation:

From the diagram, z° corresponds to

`((6)/(5)x + 10) \degree`

and

`(2x - 13) \degree`

This implies that

`z = ((6)/(5)x + 10) \degree`

and

`z = (2x - 13) \degree`

`\implies \: ((6)/(5)x + 10) \degree = (2x - 13) \degree`

Multiply through by 5:

`6x + 50 = 10x - 65`

Group similar terms:

`50 + 65 = 10x - 6x`

`125 = 4x`

`x = (125)/(4)`

`x = 31.25 \degree`

`\implies \: z = 2 * 31.25 - 13 = 49.5 \degree`

Angles on straight line are supplementary

`y + z = 180`

`49.5 + z = 180`

`z = 180 - 49.5 = 130.5 \degree`