QuestionFind the measure of $\angle ABC$ given that $\angle ABD = (4x)°$ and $\angle CBD = (5x-27)°$ .

Studdy Solution

STEP 1

Assumptions1. The line is bisected at point B, which means that angle ABD is equal to angle CBD. . The measure of angle ABD is given as $(4x)°$ .
3. The measure of angle CBD is given as $(5x-27)°$ .
4. We need to find the measure of $\angle ABC$ .

STEP 2

Since the line is bisected at point B, we can set the measures of angle ABD and angle CBD equal to each other and solve for $x$ .
$(4x)° = (5x-27)°$

STEP 3

Subtract $x$ from both sides of the equation to isolate $x$ on one side.
$0 = x -27$

STEP 4

Add $27$ to both sides of the equation to solve for $x$ .
$x =27$

STEP 5

Now that we have the value of $x$ , we can substitute it back into the expressions for the measures of angles ABD and CBD to find their actual measures.
For angle ABD $AB =4x =427 =108°$ For angle CBD $CBD =5x -27 =527 -27 =108°$

STEP 6

Now, to find the measure of $\angle ABC$ , we need to understand that it is the sum of $\angle ABD$ and $\angle CBD$ because these two angles are adjacent and share a common arm, BD.
$ABC = ABD + CBD$

STEP 7

Substitute the values of $\angle ABD$ and $\angle CBD$ into the equation.
$ABC =108° +108°$

STEP 8

Calculate the measure of $\angle ABC$ .
$ABC =216°$ The measure of $\angle ABC$ is $216°$ .

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