Note: Your teacher will grade your responses to questions 4–8 to ensure you receive proper credit for your answers.
A star-patterned quilt has a star with the angles shown. What is the value of x? The diagram is not to scale.
A five-pointed star is formed when two congruent right triangles overlap. The top triangle formed to make the top point of the star has two labeled angles. Its top angle is labeled 24 degree-sign, and its right base angle is labeled x degree-sign. The third angle of this triangle is unlabeled, but its exterior angle is labeled 105 degree-sign.
To find the value of x, we can use the fact that the angles in a triangle add up to 180 degrees.
The exterior angle of an angle in a triangle is equal to the sum of the two opposite interior angles. In this case, the exterior angle of the top angle (24 degrees) is labeled as 105 degrees.
Therefore, we can set up the equation:
24 degrees + x degrees = 105 degrees
Subtracting 24 degrees from both sides, we have:
x degrees = 105 degrees - 24 degrees
x degrees = 81 degrees
So, the value of x is 81 degrees.