Did you know?
Did you know that the measure of angle B in triangle ABC can be found using a few basic steps? Here's what you need to do:
1. Start with the given information: a line segment ACD and triangle ABC, where AC is the base of the triangle.
2. Note that angle BAC is labeled with a 72-degree sign, and angle BCD is labeled with a 113-degree sign.
3. Remember that the sum of the angles in a triangle is always equal to 180 degrees.
4. Recognize that angle B is an interior angle of triangle ABC and is not directly given.
5. Use the fact that the sum of the angles in a triangle is 180 degrees to set up an equation: angle BAC + angle B + angle BCA = 180.
6. Substitute the given values for angle BAC (72 degrees) and angle BCA (unknown) into the equation: 72 + angle B + angle BCA = 180.
7. Recognize that angle BCA can be found by subtracting angle BCD (113 degrees) from 180 degrees: angle BCA = 180 - 113 = 67 degrees.
8. Substitute the value of angle BCA (67 degrees) into the equation: 72 + angle B + 67 = 180.
9. Simplify the equation: 139 + angle B = 180.
10. Solve for angle B by subtracting 139 from both sides of the equation: angle B = 180 - 139 = 41 degrees.
11. After following these steps, you have found the measure of angle B in triangle ABC, which is 41 degrees.
