In angle ABC, ray BX is in the interior of the angle, the measure of angle ABX is 12 more than 4 times the measure of angle CBX, and the measure of angle ABC = 92 degrees.

a. Draw a diagram to represent the situation.
b. Write and solve an equation to find the measure of angle ABX and the measure of angle CBX.

Any help is much appreciated! :)

to start you should represent CBX as x. so, an equation would be 92 = x + 4x + 12. This is the equation so, 92 is the total angle, and the 12x + 4 is the ABX part. So, once you solve the problem you should get CBX=76 and ABX=16

Answer Link

MrRoyal MrRoyal · Answer 2 · 2021-09-04T07:05:24+02:00

Ray BX divides [tex]\angle ABC[/tex] into two angles [tex]\angle CBX[/tex] and [tex]\angle ABX[/tex]. The measures of CBX and ABX are 16 and 76 degrees, respectively.

Given that:

[tex]\angle ABX = 12 + 4 \times \angle CBX[/tex]

[tex]\angle ABC = 92^o[/tex]

See attachment for the diagram that represents the situation

From the attached diagram, we have:

[tex]\angle ABC = \angle ABX + \angle CBX[/tex]

Substitute [tex]\angle ABX = 12 + 4 \times \angle CBX[/tex]

[tex]92 = 12 + 4 \times \angle CBX+\angle CBX[/tex]

[tex]92 = 12 + 4\angle CBX+\angle CBX[/tex]

[tex]92 = 12 + 5\angle CBX[/tex]

Collect like terms

[tex]92 - 12 = 5\angle CBX[/tex]

[tex]80 = 5\angle CBX[/tex]

Divide both sides by 5

[tex]16 = \angle CBX[/tex]

So, we have:

[tex]\angle CBX = 16[/tex]

Recall that:

[tex]\angle ABX = 12 + 4 \times \angle CBX[/tex]

[tex]\angle ABX = 12 + 4 \times 16[/tex]

[tex]\angle ABX = 76[/tex]

Hence, the measures of CBX and ABX are 16 and 76 degrees, respectively.