Final answer:
To find the value of y in the equation (8y-6)° for one angle of a triangle and the given constant angle of 32°, we set the sum of interior angles to 180 degrees, solve the resulting equation, and find that y is 19.25.
Step-by-step explanation:
The student is asked to solve for the variable y in the context of the interior angles of a triangle. The sum of the interior angles of a triangle is 180 degrees. With two angles given, one as an expression (8y-6)° and the other as a constant 32°, we use the fact that these two angles, along with the third angle of the triangle (not given), must add up to 180 degrees to find the value of y.
Setting up the equation:
- (8y - 6)° + 32° + … = 180°
We do not have the measure of the third angle, but since the student's question includes a hint that states the sum of the angles is 90 degrees (which seems to be a typo since it should be 180 degrees for a triangle), we will assume it is a mistake and proceed to solve for y using the correct sum of angles.
Here's how to solve it:
- Add the given constant angle to the expression for the first angle: (8y - 6)° + 32° = (8y + 26)°
- Since the sum of the angles in a triangle is 180 degrees, we can make an equation: (8y + 26)° = 180°
- Subtract 26 from both sides: 8y° = 154°
- Divide both sides by 8 to solve for y: y = 19.25
Therefore, the value of y is 19.25.