the missing angles are:
1. M<A = 30 degrees
2. M<B = 163.2 degrees
3. M<C = 16.8 degrees
4. M<D = 16.8 degrees
5. M<E = 30 degrees
6. M<F = 163.2 degrees
Find the total angle measure of the triangle:
The sum of the angles in a triangle is 180 degrees. Therefore, the total angle measure of triangle ABC is:
180 degrees - 94 degrees = 86 degrees
Find the measure of angle C:
Angle C is the opposite angle to side AB, which is the longest side in the triangle. Therefore, angle C is the largest angle in the triangle. We can use the Law of Sines to find the measure of angle C:
sin(C) / AB = sin(A) / AC
We know the measure of angle A (30 degrees) and the length of side AB (62 degrees). We can also find the length of side AC by using the Pythagorean Theorem:
AC^2 = AB^2 - BC^2
We know the length of side AB (62 degrees) and the length of side BC (329 degrees). Substituting these values into the equation, we get:
AC^2 = 62^2 - 329^2
AC = 310 degrees
Now that we know the length of all three sides of the triangle, we can substitute them into the Law of Sines equation to find the measure of angle C:
sin(C) / 62 = sin(30 degrees) / 310
sin(C) = 0.286
C = 16.8 degrees
Find the measure of angles A and B:
We now know the measure of angle C and the total angle measure of the triangle. We can use these values to find the measure of angles A and B:
A + B + C = 180 degrees
A + B = 180 degrees - C
A + B = 180 degrees - 16.8 degrees
A + B = 163.2 degrees
We can also use the following relationship between the angles in a triangle:
A + B + C = 180 degrees
To find the measure of angle A, we can substitute the measures of angles B and C into the equation:
A + B + C = 180 degrees
A + 163.2 degrees = 180 degrees
A = 16.8 degrees
We can also use the same process to find the measure of angle B:
B + A + C = 180 degrees
B + 16.8 degrees = 180 degrees
B = 163.2 degrees
Find the measure of angles D, E, and F:
Angle D is the opposite angle to side AC. Angle E is the alternate interior angle to angle C. Angle F is the alternate interior angle to angle A. Therefore, the measures of angles D, E, and F are equal to the measures of angles C, A, and B, respectively.
D = C = 16.8 degrees
E = A = 30 degrees
F = B = 163.2 degrees