Triangle ABC , BC = CD and (angle ABC - angle bac ) =30, the measure of angle and is?
Ans is 15°
where does D come in with a triangle?
and what does
measure of angle and is mean?
If H is the circumcenter of BCD find each missing measure
To find the measure of angle BAC, we'll use the fact that the sum of the angles in a triangle is always 180 degrees.
Let's break down the information given:
- The sides BC and CD are equal, implying that triangle BCD is an isosceles triangle, with BC = CD.
- The difference between angle ABC and angle BAC is 30 degrees.
Now, we can proceed with solving the problem:
1. Since BC = CD, triangle BCD is isosceles. This means that angle BCD is equal to angle BDC.
2. Since the sum of the angles in a triangle is 180 degrees, we know that:
angle BAC + angle ABC + angle BCA = 180
3. Also, given that:
angle ABC - angle BAC = 30
4. We can substitute the value of angle ABC in the equation:
angle BAC + (angle BAC + 30) + angle BCA = 180
5. Combine like terms:
2 * angle BAC + angle BCA + 30 = 180
6. Simplify:
2 * angle BAC + angle BCA = 150
7. Now, let's consider triangle BAC. Angles BAC and BCA are both angles in this triangle. So:
angle BAC + angle BCA + angle ABC = 180
8. If we substitute angle ABC with angle BAC + 30 (from step 7), we get:
angle BAC + angle BCA + (angle BAC + 30) = 180
9. Combine like terms:
2 * angle BAC + angle BCA + 30 = 180
10. We can now equate this equation to the equation we derived in step 6:
2 * angle BAC + angle BCA = 2 * angle BAC + angle BCA + 30
11. Simplify:
0 = 30
12. Oops! It appears that there is no solution to this problem.
Therefore, based on the given information, we cannot determine the measure of angle BAC.