Calculate the angle x using geometric properties
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Work out the size of angle $x$. Write down the angle facts you used.
This question includes visual content: The image displays two horizontal parallel lines. A transversal line intersects both, and another segment connects them to form a triangle-like structure. At the bottom-left intersection of the lower parallel line and the transversal, there is an angle marked 65 degrees. An orange circular sector marking indicates an exterior angle of 137 degrees on the right side of the figure. An angle x is marked in green at the top vertex formed by the upper parallel line and the transversal. The parallel lines are indicated with small arrows on them.
Animated Video Solution
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Step by Step Written Solution
Hi Halimah, let's solve this geometry problem together. We need to find the size of angle x and write down the angle facts we used.
Finding Angle $x$
To make our steps perfectly clear, let's recreate this diagram on our board and look at two different ways to solve it.
Geometric Setup
First, let's notice a very elegant direct shortcut. The top and bottom horizontal lines are parallel, as shown by the matching arrows.
Method 1: Alternate Angles Direct
Because these horizontal lines are parallel, the angle x at the top-left and the angle of one hundred and thirty-seven degrees at the bottom-right are alternate interior angles.
Since alternate angles on parallel lines are equal, we immediately find that x is equal to one hundred and thirty-seven degrees.
Let's verify this using a second method by calculating the angles inside the triangle to make absolutely sure of our result.
Method 2: Triangle Verification Steps
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