Question

In AACD, if AC = AD, MZA = 3x - 4, MZC = 5x + 1, and M2D = 7x - 27, find x and the measure of each angle.

A.) x
B.) Measure of angle MZA
C.) Measure of angle MZC
D.) Measure of angle M2D

Answer 1

After setting up equations based on the given expressions for the angles, we find that x equals 5.75°. Substituting x, we find the measure of MZA is 13.25°, the measure of MZC is 29.75°, and M2D is also 13.25°.

Step-by-step explanation:

To solve for x and the measures of the angles in triangle AACD, we can set up equations based on the fact that AC is equal to AD, which implies that AACD is an isosceles triangle.

From this, we know that MZA (3x - 4) must be equal to M2D (7x - 27), as they are opposite angles of the same sides. Setting these two expressions equal gives us:

3x - 4 = 7x - 27

Solving for x, we subtract 3x from both sides and add 27 to both sides, yielding:

4x = 23

Dividing both sides by 4 yields:

x = 23/4 or 5.75

Now, we can substitute x into the expressions for each angle to find their measures:

MZA = 3(5.75) - 4 = 17.25 - 4 = 13.25°

MZC = 5(5.75) + 1 = 28.75 + 1 = 29.75°

M2D = 7(5.75) - 27 = 40.25 - 27 = 13.25°

Note that we could also confirm these angles make sense because they must sum to 180 degrees, adding up MZA, MZC, and M2D.