parallel lines

[logistic_guy]

Find the value of \(\displaystyle x\) that makes \(\displaystyle m \parallel n\).

 

[khansaheb]

Where is your attempt to solve this problem?

For problem 1, use the theorem of "interior angles"

 

[The Highlander]

63° 50° 25°

 

[logistic_guy]

Where is your attempt to solve this problem?

For problem 1, use the theorem of "interior angles"

You know the the theorem of "interior angles"?!I am surprised as I have never seen you involved in Geometry's problems!

63° 50° 25°

\(\displaystyle \bold{1.}\)

As professor khan said (not directly) the sum of these angles must be \(\displaystyle 180^{\circ}\) as a sequence of the interior angles theorem.

Therefore,

\(\displaystyle 2x^{\circ} + 54^{\circ} = 180^{\circ}\)

\(\displaystyle 2x^{\circ} = 180^{\circ} - 54^{\circ} = 126^{\circ}\)

\(\displaystyle x^{\circ} = \frac{126^{\circ}}{2} = 63^{\circ}\)

This matches what Sir The Highlander has given, so it is absolutely correct.

 

[khansaheb]

You know the the theorem of "interior angles"?!

I even know the theorem of opposite (alternate) interior angles....

 

[logistic_guy]

I even know the theorem of opposite (alternate) interior angles....

\(\displaystyle \bold{2.}\)

\(\displaystyle (3x - 5)^{\circ} = 145^{\circ}\)

\(\displaystyle 3x^{\circ} = 145^{\circ} + 5^{\circ}\)

\(\displaystyle 3x^{\circ} = 150^{\circ}\)

\(\displaystyle x^{\circ} = \frac{150^{\circ}}{3} = 50^{\circ}\)

 

[logistic_guy]

\(\displaystyle \bold{3.}\)

\(\displaystyle 88^{\circ} = (4x - 12)^{\circ}\)

\(\displaystyle 88^{\circ} + 12^{\circ} = 4x^{\circ}\)

\(\displaystyle 100^{\circ} = 4x^{\circ}\)

\(\displaystyle x^{\circ} = \frac{100^{\circ}}{4} = 25^{\circ}\)