Angle ABC measures 120 Degrees and is bisected by line BD. Find x if the measure of angle ABD is (1/2)x+5
ABD=60
x/2+5=60
x/2=55
x= ...
To find the value of x, we need to set up an equation based on the given information.
We know that angle ABC measures 120 degrees, and angle ABD is bisected by line BD. This means that angle ABD is divided into two equal angles.
Let's represent the measure of angle ABD as (1/2)x + 5 since it's given in the problem.
Since angle ABD is divided into two equal angles by line BD, each of these angles would have a measure of (1/2)((1/2)x + 5) = (1/4)x + (5/2).
Now since angle ABC measures 120 degrees, the sum of angle ABD and its bisected angle should equal 120 degrees.
Adding the measures of the two angles yields:
(1/2)x + 5 + (1/4)x + (5/2) = 120
Now, we can solve the equation for x:
(2/4)x + (20/4) + (1/4)x + (10/4) = 120
(3/4)x + (30/4) = 120
To eliminate the fractions, multiply both sides of the equation by 4:
3x + 30 = 480
Subtracting 30 from both sides of the equation:
3x = 450
Dividing both sides of the equation by 3:
x = 150
Therefore, x has a value of 150.