Question

Given mDE = 100 and mBC = 51, find the measure of angle A.

Option A: 74.5
Option B: 24.5
Option C: 75.5
Option D: 49

Answer 1

To find the measure of angle A, we can use the properties of triangles and the given angles. Subtract the given angles from 180 to find the measure of angle A.

Step-by-step explanation:

To find the measure of angle A, we need to use the properties of triangles. We know that the sum of the angles in a triangle is always 180 degrees. So, if we subtract the given angles DE and BC from 180, we can find the measure of angle A. Here's the step-by-step calculation:

1. Sum of angles in triangle ADE = mDE + mDA + mED = 180 degrees
2. sum of angles in triangle ABC = mAB + mBC + mCA = 180 degrees
3. We know that mDE = 100 and mBC = 51, so we can substitute these values into the equations: 100 + mDA + mED = 180 and mAB + 51 + mCA = 180
4. Simplify the equations: mDA + mED = 80 and mAB + mCA = 129
5. Since angle A is part of both triangles, we can set mDA = mAB and mED = mCA
6. Substitute these values into the equations: 2mDA = 80 and 2mED = 129
7. Solve for mDA and mED: mDA = 40 and mED = 64.5
8. Finally, substitute the values of mDA and mED into the equation for angle A: mDA + mED = 40 + 64.5 = 104.5 degrees