Question

a star patterned quilt has a star with the angles shown. what is the value of x? the diagram is not to scale. 105° 24° x° 81 91 99 105

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Set up the equation

Let's consider the triangle formed by the given angles. We have 24° + 105°+x = 180°.

Step3: Solve for x

First, add 24° and 105°: 24 + 105=129. Then, x = 180 - 129. So, x = 51. But this seems to be a wrong - approach. Let's consider the exterior - angle property. An exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. The exterior angle of the triangle with the given 105° and x° angles is 105°. One of the non - adjacent interior angles is 24°. So, 105=x + 24.

Step4: Rearrange the equation to solve for x

Subtract 24 from both sides of the equation: x=105 - 24.
x = 81

Answer:

81