Question

kathryns family has a light on the porch that shines on the backyard at night, as shown by the unknown angle. kathryn says she can solve the expression 180+(70 - 25) to find the measure of the unknown angle cast by the light. why is kathryn incorrect? choose one option from each drop - down menu to answer the question. solving kathryns expression gives an angle measure that is choose.... however, the angle cast by the light is choose... angle. kathryn should have choose... to find the unknown angle measure, which is choose...

Explanation:

Step1: Recall angle - sum property

The sum of angles on a straight - line is 180°. The unknown angle in the triangle can be found using the fact that the exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step2: Analyze Kathryn's expression

Kathryn's expression 180+(70 - 25) is incorrect. First, solve 180+(70 - 25)=180 + 45=225. But angles in a triangle and related to a straight - line situation do not follow this calculation.

Step3: Correct way to find the angle

The correct way is to use 180-(70 + 25). Because the three angles on the straight - line must sum to 180°. Let the unknown angle be \(x\). We have \(x+70 + 25=180\), so \(x = 180-(70 + 25)=85\).

Answer:

Solving Kathryn's expression gives an angle measure that is much larger than any reasonable angle in this context. However, the angle cast by the light is an interior angle of a triangle formed by the light rays. Kathryn should have subtracted the sum of the given angles from 180 to find the unknown angle measure, which is 85°.