Answer:
To find the measure of angle C in the inscribed quadrilateral ABCD, we can use the fact that the sum of opposite angles in an inscribed quadrilateral is equal to (180^\circ). Given the expressions for the angles:
Angle A: (x + 15^\circ)
Angle B: (x + 10^\circ)
Angle C: (x + 24^\circ)
We can set up the equation for the sum of angles A and C:
[ (x + 15^\circ) + (x + 24^\circ) = 180^\circ ]
Solving for (x):
[ 2x + 39^\circ = 180^\circ ] [ 2x = 141^\circ ] [ x = 70.5^\circ ]
Now, we can find the measure of angle C:
[ x + 24^\circ = 70.5^\circ + 24^\circ = 94.5^\circ ]
Therefore, the measure of angle C is (94.5^\circ). If you have any more questions or need further assistance, feel free to ask!
