Answer:
the measure of angle a is 51.43 degrees, the measure of angles C and E is also 51.43 degrees. The measure of angle D is 77.14 degrees.
Explanation:
Since CDE is an isosceles triangle with the base ED, the two angles at C and E are equal. Let's call this angle a. This means that the angles at D and E are also equal and have a measure of 180 - 2a.
We know that the measure of angle D is 4x + 23. Since the angles at D and E are equal, the measure of angle E is also 4x + 23. Therefore, the measure of angle a is 2x + 23.
To find the measure of each angle in the triangle, we need to use the fact that the sum of the angles in a triangle is 180 degrees. Since we already know the measure of angle D and angle E, we can use this information to find the measure of angle C.
Since the sum of the angles in the triangle is 180 degrees, we can write the following equation:
a + (180 - 2a) + (180 - 2a) = 180
Solving for a, we get:
a = 180 - 2(180 - 2a)
a = 360 - 4(180 - 2a)
a = 360 - 720 + 8a
a = -360 + 8a
7a = 360
a = 51.43 degrees
Since the measure of angle a is 51.43 degrees, the measure of angles C and E is also 51.43 degrees. The measure of angle D is 4x + 23, as given in the problem statement.