To find the value of x, we can use the fact that the sum of the angles in a triangle is 180 degrees.
The exterior angle of an angle in a triangle is equal to the sum of the other two interior angles. In this case, the exterior angle is 105 degrees, and one of the interior angles is 24 degrees. Let's call the third angle of the triangle y degrees.
Therefore, we can write the equation:
105 = 24 + y
To solve for y, we subtract 24 from both sides:
81 = y
So, the third angle of the triangle is 81 degrees.
Since the sum of the angles in a triangle is 180 degrees, we can use this information to find the value of x:
180 = 81 + 90 + x
Subtracting 81 and 90 from both sides, we have:
180 - 81 - 90 = x
x = 9
Therefore, the value of x is 9 degrees.
Short Answer
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.
1 answer
1 answer