BD bisects angle ABC , m angle ABD= angle(3x)^ , and m angle ABC=42^ What is the value of x?
Since BD bisects angle ABC, it means that angle ABD and angle DBC are congruent. We know that m angle ABD = angle (3x)^ and m angle ABC = 42^.
Given that m angle ABC = 42^, we can set up the following equation:
angle (3x)^ + angle (3x)^ = 42^
To find the value of x, we need to solve this equation.
First, simplify the equation:
6x = 42
Divide both sides of the equation by 6:
6x/6 = 42/6
x = 7
Therefore, the value of x is 7.
To find the value of x in this problem, we can use the property of angles in a triangle.
Since BD bisects angle ABC, we know that angle ABD and angle CBD are equal in measure.
Let's set the measure of angle ABD as 3x degrees, and the measure of angle CBD as 3x degrees as well.
Since the sum of the angles in a triangle is 180 degrees, we can write the following equation:
Angle ABD + Angle ABC + Angle CBD = 180
Substituting the values we know into the equation:
3x + 42 + 3x = 180
Combine like terms:
6x + 42 = 180
Now, we can isolate x by subtracting 42 from both sides of the equation:
6x = 180 - 42
6x = 138
Finally, divide both sides of the equation by 6 to solve for x:
x = 138/6
Simplifying the division:
x = 23
Therefore, the value of x is 23.
since BD bisects the angle,
2*3x = 42
x = 7