Find the measure of angle DBC if the measure of angle ABD is 36 degrees and the measure of angle ABC is 74 degrees.
To find the measure of angle DBC, we need to use the fact that the sum of the angles in a triangle is 180 degrees.
Step 1: Find the measure of angle BDC.
Since the sum of the angles in triangle ABC is 180 degrees, we can subtract the measures of angles ABD and ABC from 180:
180 - 36 - 74 = 70 degrees
Step 2: Find the measure of angle DBC.
Since angles DBC and BDC together form a straight angle (180 degrees), we can subtract the measure of angle BDC from 180:
180 - 70 = 110 degrees
Therefore, the measure of angle DBC is 110 degrees.
To find the measure of angle DBC, we need to use the fact that the sum of angles in a triangle is 180 degrees. In triangle ABC, angle ABC is given as 74 degrees, and angle ABD is given as 36 degrees.
We know that angle ABC + angle ABD + angle DBC = 180 degrees.
Substituting the given values into the equation, we have:
74 degrees + 36 degrees + angle DBC = 180 degrees.
Adding the given angles, we get:
110 degrees + angle DBC = 180 degrees.
Now, isolate angle DBC by subtracting 110 degrees from both sides of the equation:
angle DBC = 180 degrees - 110 degrees.
Simplifying the equation, we get:
angle DBC = 70 degrees.
Therefore, the measure of angle DBC is 70 degrees.