QuestionGiven angles: $\angle B = 30^\circ$ , $\angle C = 125^\circ$ , find $x+y$ where $\angle A = y^\circ$ and $\angle D = x^\circ$ .

Studdy Solution

STEP 1

Assumptions1. The line segment $\overline{AB}$ is perpendicular to $\overline{AD}$ , which means angle $A$ is a right angle and measures $90^\circ$ . . Points $A$ , $C$ , and are collinear, which means they lie on the same line.
3. The measure of angle $B$ is $30^\circ$.
4. The measure of angle $A$ is $y^\circ$.
5. The measure of angle $C$ is $125^\circ$.
6. The measure of angle is $x^\circ$ .

STEP 2

Since $\overline{AB}$ is perpendicular to $\overline{AD}$ , the measure of angle $A$ is $90^\circ$ . So, $y =90^\circ$ .

STEP 3

In triangle $ABC$ , the sum of the measures of the interior angles is $180^\circ$ . So, we have the equation $\angle B + \angle A + \angle C =180^\circ$

STEP 4

Substitute the given values for the measures of angles $B$ , $A$ , and $C$ into the equation.
$30^\circ + y +125^\circ =180^\circ$

STEP 5

implify the equation.
$y +155^\circ =180^\circ$

STEP 6

Subtract $155^\circ$ from both sides of the equation to solve for $y$ .
$y =180^\circ -155^\circ$

STEP 7

Calculate the value of $y$ .
$y =25^\circ$

STEP 8

The measure of angle $$ is the same as the measure of angle $C$ because they are corresponding angles on a line. So, $x =125^\circ$.

STEP 9

Now that we have the values for $x$ and $y$ , we can find the sum $x + y$ .
$x + y =125^\circ +25^\circ$

STEP 10

Calculate the sum $x + y$ .
$x + y =150^\circ$ The degree measure of $x + y$ is $150^\circ$ .

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QuestionGiven angles: $\angle B = 30^\circ$ , $\angle C = 125^\circ$ , find $x+y$ where $\angle A = y^\circ$ and $\angle D = x^\circ$ .

Studdy Solution

STEP 1

STEP 2

Since $\overline{AB}$ is perpendicular to $\overline{AD}$ , the measure of angle $A$ is $90^\circ$ . So, $y =90^\circ$ .

STEP 3

In triangle $ABC$ , the sum of the measures of the interior angles is $180^\circ$ . So, we have the equation $\angle B + \angle A + \angle C =180^\circ$

STEP 4

Substitute the given values for the measures of angles $B$ , $A$ , and $C$ into the equation.
$30^\circ + y +125^\circ =180^\circ$

STEP 5

implify the equation.
$y +155^\circ =180^\circ$

STEP 6

Subtract $155^\circ$ from both sides of the equation to solve for $y$ .
$y =180^\circ -155^\circ$

STEP 7

Calculate the value of $y$ .
$y =25^\circ$

STEP 8

The measure of angle $$ is the same as the measure of angle $C$ because they are corresponding angles on a line. So, $x =125^\circ$.

STEP 9

Now that we have the values for $x$ and $y$ , we can find the sum $x + y$ .
$x + y =125^\circ +25^\circ$

STEP 10

Calculate the sum $x + y$ .
$x + y =150^\circ$ The degree measure of $x + y$ is $150^\circ$ .

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QuestionGiven angles: ∠B=30∘\angle B = 30^\circ∠B=30∘, ∠C=125∘\angle C = 125^\circ∠C=125∘, find x+yx+yx+y where ∠A=y∘\angle A = y^\circ∠A=y∘ and ∠D=x∘\angle D = x^\circ∠D=x∘.

Studdy Solution

STEP 1

STEP 2

Since AB‾\overline{AB}AB is perpendicular to AD‾\overline{AD}AD, the measure of angle AAA is 90∘90^\circ90∘. So, y=90∘y =90^\circy=90∘.

STEP 3

In triangle ABCABCABC, the sum of the measures of the interior angles is 180∘180^\circ180∘. So, we have the equation∠B+∠A+∠C=180∘\angle B + \angle A + \angle C =180^\circ∠B+∠A+∠C=180∘

STEP 4

Substitute the given values for the measures of angles BBB, AAA, and CCC into the equation.30∘+y+125∘=180∘30^\circ + y +125^\circ =180^\circ30∘+y+125∘=180∘

STEP 5

implify the equation.y+155∘=180∘y +155^\circ =180^\circy+155∘=180∘

STEP 6

Subtract 155∘155^\circ155∘ from both sides of the equation to solve for yyy.y=180∘−155∘y =180^\circ -155^\circy=180∘−155∘

STEP 7

Calculate the value of yyy.y=25∘y =25^\circy=25∘

STEP 8

The measure of angle $$ is the same as the measure of angle $C$ because they are corresponding angles on a line. So, $x =125^\circ$.

STEP 9

Now that we have the values for xxx and yyy, we can find the sum x+yx + yx+y.x+y=125∘+25∘x + y =125^\circ +25^\circx+y=125∘+25∘

STEP 10

Calculate the sum x+yx + yx+y.x+y=150∘x + y =150^\circx+y=150∘The degree measure of x+yx + yx+y is 150∘150^\circ150∘.

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QuestionGiven angles: $\angle B = 30^\circ$ , $\angle C = 125^\circ$ , find $x+y$ where $\angle A = y^\circ$ and $\angle D = x^\circ$ .

Since $\overline{AB}$ is perpendicular to $\overline{AD}$ , the measure of angle $A$ is $90^\circ$ . So, $y =90^\circ$ .

In triangle $ABC$ , the sum of the measures of the interior angles is $180^\circ$ . So, we have the equation $\angle B + \angle A + \angle C =180^\circ$

Substitute the given values for the measures of angles $B$ , $A$ , and $C$ into the equation.
$30^\circ + y +125^\circ =180^\circ$

implify the equation.
$y +155^\circ =180^\circ$

Subtract $155^\circ$ from both sides of the equation to solve for $y$ .
$y =180^\circ -155^\circ$

Calculate the value of $y$ .
$y =25^\circ$

Now that we have the values for $x$ and $y$ , we can find the sum $x + y$ .
$x + y =125^\circ +25^\circ$

Calculate the sum $x + y$ .
$x + y =150^\circ$ The degree measure of $x + y$ is $150^\circ$ .