Math

QuestionFind mABCm \angle ABC if mABC=6x4m \angle ABC = 6x - 4, mCBD=3x+2m \angle CBD = 3x + 2, and mABD=34m \angle ABD = 34.

Studdy Solution

STEP 1

Assumptions1. The measure of angle ABC is given by 6x46x -4 . The measure of angle CBD is given by 3x+3x +
3. The measure of angle ABD is given as 3434
4. Angle ABD and angle CBD are adjacent angles and together form angle ABC. This is based on the angle addition postulate, which states that the measure of an angle formed by two adjacent angles is equal to the sum of the measures of the two angles.

STEP 2

Based on the angle addition postulate, we can write the equationmABC=mABD+mCBDm \angle ABC = m \angle ABD + m \angle CBD

STEP 3

Substitute the given expressions for the measures of the angles into the equation.
6x=34+(3x+2)6x - =34 + (3x +2)

STEP 4

implify the equation by distributing and combining like terms.
6x4=34+3x+26x -4 =34 +3x +2

STEP 5

Combine the constant terms on the right side of the equation.
x4=3x+36x -4 =3x +36

STEP 6

Subtract 3x3x from both sides of the equation to isolate the variable on one side.
6x3x=36+46x -3x =36 +4

STEP 7

implify the left side of the equation.
3x=36+43x =36 +4

STEP 8

implify the right side of the equation.
3x=403x =40

STEP 9

Divide both sides of the equation by3 to solve for xx.
x=40/3x =40 /3

STEP 10

Calculate the value of xx.
x=13.33x =13.33

STEP 11

Substitute x=13.33x =13.33 into the expression for mABCm \angle ABC to find the measure of angle ABC.
mABC=6x4m \angle ABC =6x -4

STEP 12

Substitute x=.33x =.33 into the expression.
mABC=6(.33)4m \angle ABC =6(.33) -4

STEP 13

Calculate the measure of angle ABC.
mABC=79.98m \angle ABC =79.98The measure of angle ABC is approximately 8080 degrees.

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