Question

1. Find the value of x. The diagram is not to scale. Lines F and G are parallel.

Answer 1

(1)

we are given that

f and g are parallel lines

so, sum of both angles must be 180

$5x+9x+26=180$

now, we can solve for x

$14x+26=180$

Subtract both sides by 26

$14x+26-26=180-26$

$14x=154$

$x=11$...........Answer

(2)

we are given that

l and m are parallel lines

so, alternate angles must be equal

so, we get

$x=28$...........Answer

Answer 2

Answer:

Part 1:

we have to find the value of x

we have been given the lines f and g are parallel

Interior angles on the same side are supplementary.

Hence, the two given angles will be equal to 180

$5x^{\circ}+9x^{\circ}+26^{\circ}=180^{\circ}$

$14x^{\circ}=180^{\circ}-26^{\circ}$

$14x^{\circ}=154^{\circ}$

$x=11^{\circ}$

Therefore, Option B is correct.

Part 2:

We have to find x

l and m are parallel

Two parallel lines are cut by Transverse line

And angles on the opposite sides that are alternate interior angles are equal

Hence, $x=28^{\circ}$

Therefore, option A is correct.

Part 3:

a. m∠5=$40^{\circ}$

and m∠2=$140^{\circ}$

b. m∠5+m∠2=$40^{\circ}+140^{\circ}=180^{\circ}$

c.∠5 and ∠2 are supplementary because they are $180^{\circ}$

d.∠5 and ∠2 are same side interior angles since, they are $180^{\circ}$

e. a || b since, a is  $180^{\circ}$  and b is also $180^{\circ}$.