The base of a pentagon lies on ray AB as shown.
An illustration showing a pentagon lying on ray AB, which when extended forms an exterior angle and is marked as 2x plus 14 degrees. The interior angle next to this exterior angle measures 7x plus 13 degrees.
Determine which statements are true
Based on the given information, we know that the exterior angle formed by extending ray AB is 2x + 14 degrees, and the adjacent interior angle is 7x + 13 degrees.
To determine which statements are true, we can use the property that the exterior angle of a polygon is equal to the sum of the two remote interior angles. Therefore, we can set up the following equation:
2x + 14 = 7x + 13
Subtracting 2x from both sides gives:
14 = 5x + 13
Subtracting 13 from both sides gives:
1 = 5x
Dividing by 5 gives:
x = 1/5
Now that we have found the value of x, we can substitute it back into the expressions for the interior and exterior angles to find their measures:
Interior angle: 7(1/5) + 13 = 7/5 + 13 = 7/5 + 65/5 = 72/5 = 14.4 degrees
Exterior angle: 2(1/5) + 14 = 2/5 + 14 = 2/5 + 70/5 = 72/5 = 14.4 degrees
Therefore, the exterior angle measures 14.4 degrees and the interior angle measures 14.4 degrees as well.