Math / Geometry

QuestionIn the figure below, $l \| m$ . Find $x$ . $x=$

Studdy Solution

STEP 1

1. The lines $l$ and $m$ are parallel.
2. The sum of angles in a triangle is $180^\circ$ .
3. The angles inside the triangle are $141^\circ$ , $x^\circ$ , and $48^\circ$ .

STEP 2

1. Use the properties of parallel lines and transversals.
2. Apply the triangle angle sum property to find $x$ .

STEP 3

Recognize that the angle $141^\circ$ is an exterior angle to the triangle formed by the transversal. The exterior angle is equal to the sum of the two non-adjacent interior angles of the triangle.

STEP 4

Use the triangle angle sum property. The sum of the interior angles of a triangle is $180^\circ$ . Therefore, we have:
$141^\circ + x^\circ + 48^\circ = 180^\circ$

STEP 5

Solve for $x$ by subtracting the known angles from $180^\circ$ :
$x^\circ = 180^\circ - 141^\circ - 48^\circ$

STEP 6

Calculate the value of $x$ :
$x^\circ = 180^\circ - 189^\circ$ $x^\circ = -9^\circ$
This result is incorrect, indicating a misinterpretation of the angle relationships. Let's correct this.

STEP 7

Re-evaluate the setup. The correct relationship is:
The exterior angle $141^\circ$ should equal the sum of the opposite interior angles $x^\circ$ and $48^\circ$ .
$141^\circ = x^\circ + 48^\circ$

STEP 8

Solve for $x$ :
$x^\circ = 141^\circ - 48^\circ$ $x^\circ = 93^\circ$
The value of $x$ is:
$\boxed{93^\circ}$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms