Question

find the range of possible values for y.
the range of possible values is \square < y < \square.\
(simplify your answers. type integers or decimals.)

Explanation:

Step1: Apply triangle angle inequality

In the triangle formed by the equal sides and diagonal, the larger angle is opposite the longer side. First, use the property that the angle $(2y-1)^\circ$ must be greater than $24^\circ$ (since it is opposite the side of length 10, which is longer than the side of length 8 opposite $24^\circ$):
$$2y - 1 > 24$$

Step2: Solve lower bound inequality

Isolate $y$ by adding 1 to both sides, then divide by 2:
$$2y > 25 \implies y > 12.5$$

Step3: Apply angle sum constraint

The sum of the two angles must be less than $180^\circ$ (they are two angles in a triangle, so their sum cannot exceed $180^\circ$):
$$2y - 1 + 24 < 180$$

Step4: Solve upper bound inequality

Simplify and isolate $y$:
$$2y + 23 < 180 \implies 2y < 157 \implies y < 78.5$$

Answer:

$12.5 < y < 78.5$