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°.

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

z=180°-(135.50)°

z=(44.50)°

$z=44\frac{1}{2}^{\circ}$

Answer 2

Answer:

x=31.25°

y=49.5°

z=130.5°

Step-by-step explanation:

From the diagram, z° corresponds to

$(\frac{6}{5}x + 10) \degree$

and

$(2x - 13) \degree$

This implies that

$z = (\frac{6}{5}x + 10) \degree$

and

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

$\implies \: (\frac{6}{5}x + 10) \degree = (2x - 13) \degree$

Multiply through by 5:

$6x + 50 = 10x - 65$

Group similar terms:

$50 + 65 = 10x - 6x$

$125 = 4x$

$x = \frac{125}{4}$

$x = 31.25 \degree$

$\implies \: z = 2 \times 31.25 - 13 = 49.5 \degree$

Angles on straight line are supplementary

$y + z = 180$

$49.5 + z = 180$

$z = 180 - 49.5 = 130.5 \degree$