BD bisects angle ABC, measure of angle ABC=5x-4, and measure of angle CBD=2x+10 angle ABC is a(n) _ angle
To determine the type of angle ABC, we need to find its measure using the given information.
We know that BD bisects angle ABC, which means that angle ABC is divided into two equal angles. Therefore, we can set up an equation to represent this:
Measure of angle ABC = Measure of angle CBD
Since the measure of angle ABC is given as 5x-4 and the measure of angle CBD is given as 2x+10, we can equate these two expressions:
5x-4 = 2x+10
To solve this equation, we need to isolate the variable x. Starting with the given equation:
5x - 2x = 10 + 4
3x = 14
Dividing both sides of the equation by 3:
x = 14/3
Now that we know the value of x, we can substitute it back into the expression for the measure of angle ABC:
Measure of angle ABC = 5x - 4
= 5(14/3) - 4
Evaluating the expression:
= 70/3 - 4
= (70 - 12)/3
= 58/3
Therefore, the measure of angle ABC is 58/3.
Based on the measure of angle ABC, we can classify it as a "non-right" angle or a "not 90 degrees" angle.
To determine the type of angle that angle ABC is, we need to examine its measure and compare it to the definitions of different types of angles. In this case, we are given that angle ABC is bisected by line segment BD.
The measure of angle ABC is given as 5x-4, and the measure of angle CBD is given as 2x+10. Since BD bisects angle ABC, this means that the measure of angle ABC is split equally into two parts by BD.
To find the value of x, we can set the measure of angle ABC equal to the sum of the measures of the two smaller angles (CBD and the other half of angle ABC, hence also CBD). So, we have:
5x - 4 = (2x + 10) + (2x + 10)
Simplifying this equation yields:
5x - 4 = 4x + 20
Next, we solve for x:
5x - 4x = 20 + 4
x = 24
Now that we have the value of x, we can substitute it back into the measures of the angles:
Angle ABC = 5x - 4 = 5(24) - 4 = 116 degrees
Angle CBD = 2x + 10 = 2(24) + 10 = 58 degrees
Since angle ABC is bisected by BD, it is split equally into two smaller angles, one of which is angle CBD. Therefore, angle ABC is a supplementary angle.
Acute
Solve for x from the equation:
5x-4 = 2(2x+10)
5x-4 = 4x + 20
5x-4x = 20+4
x=24
so angle ABC = 5(24)-4 = 120-4=116 degrees.
What kind of angle is angle ABC?