To find the value of x, we can use the fact that the sum of the angles in a triangle is 180 degrees.
Since the top angle of the triangle is labeled as 24 degrees, and the exterior angle of the triangle is labeled as 105 degrees, we can find the third angle of the triangle by subtracting the exterior angle from 180 degrees.
Third angle = 180 degrees - exterior angle
Third angle = 180 degrees - 105 degrees
Third angle = 75 degrees
Now, we can use the fact that the sum of the angles in a triangle is 180 degrees to find the value of x.
Sum of angles in the triangle = top angle + right base angle + third angle
180 degrees = 24 degrees + x degrees + 75 degrees
Now, we can solve for x. Subtracting 24 degrees and 75 degrees from both sides of the equation, we have:
180 degrees - 24 degrees - 75 degrees = x degrees
81 degrees = x
Therefore, the value of x is 81 degrees.
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.
1 answer
1 answer