Finding an unkown angle of a triangle
Step 1: drawing the description
We are going to start drawing the described situation: we have the triangle ΔBCD with two congruent sides
and that m∠B = 139º:
Step 2: analysis
Analyzing the symmetry of the figure, we can conclude that the angles m∠D and m∠C are equal since the sides BC and DB are congruent (if m∠D and m∠C were not equal, BC and DB would not be congruent):
m∠D = m∠C
Step 3: writing an equation
If we add all the inner angles of a triangle the result is 180º, then:
m∠B + m∠C + m∠D = 180º
Now, we have an equation that we can use to find m∠D:
m∠B + m∠C + m∠D = 180º
↓ since m∠D = m∠C
m∠B + m∠D + m∠D = 180º
m∠B + 2 · m∠D = 180º
↓ since m∠B = 139º
139º + 2 · m∠D = 180º
Step 4: solving the equation
We want to solve the equation
139º + 2 · m∠D = 180º
in order to do so, we want to "leave m∠D alone on the left side".
139º + 2 · m∠D = 180º
↓ taking 139º to the right side
2 · m∠D = 180º - 139º = 41º
2 · m∠D = 41º
↓ taking 2 to the right side
m∠D = 41º/2 = 20.5º
m∠D = 20.5º
Answer: m∠D = 20.5º