Question

Find the value of the variable in each figure. explain your reasoning

Answer 1

Answer:

Number 7)  x=14 and y=37

Number 8)  x=28 and y=23

Explanation:

Number 7) Please see fig 1 in the attachment for naming of angle.

As per diagram line b||c and their transverse line a.

Using line and angle concepts.

$\angle 1=3x$ {Corresponding angles of parallel line b||c}

$\angle 1+(9x+12)=180^{\circ}$ {Supplementary angle of straight line}

$\therefore 3x+9x+12=180$

Now combine the like term and solve for x and we get,

12x=180-12

x=14

For line a, 4y-10+3x=180 {Supplementary angle of straight line}

where, x=14

So, we get 4y-10+3(14)=180

4y=180-32

y=37

Number 8) Please see fig 2 in the attachment for naming of angles.

As per given diagram a||b||c and line d is transversal of all three line.

Using line and angle concepts.

$\angle 1=3y$ {Corresponding angles of parallel line a||b}

$\angle 1+(5y-4)=180^{\circ}$ {Supplementary angle of straight line}

3y+5y-4=180

8y=184

y=23

3y=2x+13 {Corresponding angles of parallel line b||c}

we calculated y=23 substitute into above equation and we get

3(23)=2x+13

2x=69-13

x=28