QuestionIf $BD$ bisects $\angle ABC$ , find $m \angle ABD$ , $m \angle CBD$ , and $m \angle ABC$ with $m \angle ABC = (25x+34)^\circ$ and $m \angle CBD = (11x+22)^\circ$ .

Studdy Solution

STEP 1

Assumptions1. Line segment $BD$ bisects $\angle ABC$ . . The measure of $\angle ABC = (25x+34)^\circ$ .
3. The measure of $\angle CBD = (11x+22)^\circ$ .

STEP 2

Since $BD$ bisects $\angle ABC$ , the measure of $\angle ABD$ is equal to the measure of $\angle CBD$ . We can set up the equation $m \angle ABD = m \angle CBD$

STEP 3

Substitute the given expressions for $m \angle ABD$ and $m \angle CBD$ into the equation $(25x+34)^\circ = (11x+22)^\circ$

STEP 4

olve for $x$ by subtracting $11x$ from both sides of the equation $14x +34 =22$

STEP 5

Subtract $34$ from both sides of the equation $14x = -12$

STEP 6

Divide both sides of the equation by $14$ to solve for $x$ $x = -\frac{12}{14} = -\frac{6}{}$

STEP 7

Now that we have the value of $x$ , we can substitute it back into the expressions for $m \angle ABD$ and $m \angle CBD$ to find their measures $m \angle ABD =25(-\frac{6}{7}) +34 = -\frac{150}{7} +34 = -\frac{86}{7} = -12.29^\circ$ $m \angle CBD =11(-\frac{6}{7}) +22 = -\frac{66}{7} +22 = -\frac{44}{7} = -6.29^\circ$

STEP 8

The measures of $\angle ABD$ and $\angle CBD$ are negative, which is not possible for an angle measure. This means that there is no solution for the given problem.

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QuestionIf $BD$ bisects $\angle ABC$ , find $m \angle ABD$ , $m \angle CBD$ , and $m \angle ABC$ with $m \angle ABC = (25x+34)^\circ$ and $m \angle CBD = (11x+22)^\circ$ .

Studdy Solution

STEP 1

Assumptions1. Line segment $BD$ bisects $\angle ABC$ . . The measure of $\angle ABC = (25x+34)^\circ$ .
3. The measure of $\angle CBD = (11x+22)^\circ$ .

STEP 2

Since $BD$ bisects $\angle ABC$ , the measure of $\angle ABD$ is equal to the measure of $\angle CBD$ . We can set up the equation $m \angle ABD = m \angle CBD$

STEP 3

Substitute the given expressions for $m \angle ABD$ and $m \angle CBD$ into the equation $(25x+34)^\circ = (11x+22)^\circ$

STEP 4

olve for $x$ by subtracting $11x$ from both sides of the equation $14x +34 =22$

STEP 5

Subtract $34$ from both sides of the equation $14x = -12$

STEP 6

Divide both sides of the equation by $14$ to solve for $x$ $x = -\frac{12}{14} = -\frac{6}{}$

STEP 7

STEP 8

The measures of $\angle ABD$ and $\angle CBD$ are negative, which is not possible for an angle measure. This means that there is no solution for the given problem.

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QuestionIf BDBDBD bisects ∠ABC\angle ABC∠ABC, find m∠ABDm \angle ABDm∠ABD, m∠CBDm \angle CBDm∠CBD, and m∠ABCm \angle ABCm∠ABC with m∠ABC=(25x+34)∘m \angle ABC = (25x+34)^\circm∠ABC=(25x+34)∘ and m∠CBD=(11x+22)∘m \angle CBD = (11x+22)^\circm∠CBD=(11x+22)∘.

Studdy Solution

STEP 1

Assumptions1. Line segment BDBDBD bisects ∠ABC\angle ABC∠ABC. . The measure of ∠ABC=(25x+34)∘\angle ABC = (25x+34)^\circ∠ABC=(25x+34)∘.3. The measure of ∠CBD=(11x+22)∘\angle CBD = (11x+22)^\circ∠CBD=(11x+22)∘.

STEP 2

Since BDBDBD bisects ∠ABC\angle ABC∠ABC, the measure of ∠ABD\angle ABD∠ABD is equal to the measure of ∠CBD\angle CBD∠CBD. We can set up the equationm∠ABD=m∠CBDm \angle ABD = m \angle CBDm∠ABD=m∠CBD

STEP 3

Substitute the given expressions for m∠ABDm \angle ABDm∠ABD and m∠CBDm \angle CBDm∠CBD into the equation(25x+34)∘=(11x+22)∘(25x+34)^\circ = (11x+22)^\circ(25x+34)∘=(11x+22)∘

STEP 4

olve for xxx by subtracting 11x11x11x from both sides of the equation14x+34=2214x +34 =2214x+34=22

STEP 5

Subtract 343434 from both sides of the equation14x=−1214x = -1214x=−12

STEP 6

Divide both sides of the equation by 141414 to solve for xxxx=−1214=−6x = -\frac{12}{14} = -\frac{6}{}x=−1412​=−6​

STEP 7

STEP 8

The measures of ∠ABD\angle ABD∠ABD and ∠CBD\angle CBD∠CBD are negative, which is not possible for an angle measure. This means that there is no solution for the given problem.

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QuestionIf $BD$ bisects $\angle ABC$ , find $m \angle ABD$ , $m \angle CBD$ , and $m \angle ABC$ with $m \angle ABC = (25x+34)^\circ$ and $m \angle CBD = (11x+22)^\circ$ .

Assumptions1. Line segment $BD$ bisects $\angle ABC$ . . The measure of $\angle ABC = (25x+34)^\circ$ .
3. The measure of $\angle CBD = (11x+22)^\circ$ .

Since $BD$ bisects $\angle ABC$ , the measure of $\angle ABD$ is equal to the measure of $\angle CBD$ . We can set up the equation $m \angle ABD = m \angle CBD$

Substitute the given expressions for $m \angle ABD$ and $m \angle CBD$ into the equation $(25x+34)^\circ = (11x+22)^\circ$

olve for $x$ by subtracting $11x$ from both sides of the equation $14x +34 =22$

Subtract $34$ from both sides of the equation $14x = -12$

Divide both sides of the equation by $14$ to solve for $x$ $x = -\frac{12}{14} = -\frac{6}{}$

The measures of $\angle ABD$ and $\angle CBD$ are negative, which is not possible for an angle measure. This means that there is no solution for the given problem.