Math / Geometry

QuestionFind the values of $x$ and $y$ .

Studdy Solution

STEP 1

1. The lines intersect, forming four angles around the intersection point.
2. Vertically opposite angles are equal.
3. Adjacent angles formed by intersecting lines are supplementary, meaning they add up to 180°.

STEP 2

1. Determine the value of $y$ using the property of vertically opposite angles.
2. Determine the value of $x$ using the property of supplementary angles.

STEP 3

Using the property of vertically opposite angles, we know that $y$ is equal to the angle vertically opposite to it, which is 78°.
$y = 78^\circ$

STEP 4

Using the property of supplementary angles, we know that $x$ and 78° are adjacent angles formed by intersecting lines, and they must add up to 180°.
$x + 78^\circ = 180^\circ$

STEP 5

Solve for $x$ .
$x = 180^\circ - 78^\circ$

STEP 6

Calculate the value of $x$ .
$x = 102^\circ$
Solution: The values of $x$ and $y$ are: $x = 102^\circ$ $y = 78^\circ$

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QuestionFind the values of $x$ and $y$ .

Studdy Solution

STEP 1

1. The lines intersect, forming four angles around the intersection point.
2. Vertically opposite angles are equal.
3. Adjacent angles formed by intersecting lines are supplementary, meaning they add up to 180°.

STEP 2

1. Determine the value of $y$ using the property of vertically opposite angles.
2. Determine the value of $x$ using the property of supplementary angles.

STEP 3

Using the property of vertically opposite angles, we know that $y$ is equal to the angle vertically opposite to it, which is 78°.
$y = 78^\circ$

STEP 4

Using the property of supplementary angles, we know that $x$ and 78° are adjacent angles formed by intersecting lines, and they must add up to 180°.
$x + 78^\circ = 180^\circ$

STEP 5

Solve for $x$ .
$x = 180^\circ - 78^\circ$

STEP 6

Calculate the value of $x$ .
$x = 102^\circ$
Solution: The values of $x$ and $y$ are: $x = 102^\circ$ $y = 78^\circ$

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QuestionFind the values of xxx and yyy.

Studdy Solution

STEP 1

1. The lines intersect, forming four angles around the intersection point.2. Vertically opposite angles are equal.3. Adjacent angles formed by intersecting lines are supplementary, meaning they add up to 180°.

STEP 2

1. Determine the value of yyy using the property of vertically opposite angles.2. Determine the value of xxx using the property of supplementary angles.

STEP 3

Using the property of vertically opposite angles, we know that yyy is equal to the angle vertically opposite to it, which is 78°.y=78∘ y = 78^\circ y=78∘

STEP 4

Using the property of supplementary angles, we know that xxx and 78° are adjacent angles formed by intersecting lines, and they must add up to 180°.x+78∘=180∘ x + 78^\circ = 180^\circ x+78∘=180∘

STEP 5

Solve for xxx.x=180∘−78∘ x = 180^\circ - 78^\circ x=180∘−78∘

STEP 6

Calculate the value of xxx.x=102∘ x = 102^\circ x=102∘Solution: The values of xxx and yyy are: x=102∘ x = 102^\circ x=102∘ y=78∘ y = 78^\circ y=78∘

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QuestionFind the values of $x$ and $y$ .

1. The lines intersect, forming four angles around the intersection point.
2. Vertically opposite angles are equal.
3. Adjacent angles formed by intersecting lines are supplementary, meaning they add up to 180°.

1. Determine the value of $y$ using the property of vertically opposite angles.
2. Determine the value of $x$ using the property of supplementary angles.

Using the property of vertically opposite angles, we know that $y$ is equal to the angle vertically opposite to it, which is 78°.
$y = 78^\circ$

Using the property of supplementary angles, we know that $x$ and 78° are adjacent angles formed by intersecting lines, and they must add up to 180°.
$x + 78^\circ = 180^\circ$

Solve for $x$ .
$x = 180^\circ - 78^\circ$

Calculate the value of $x$ .
$x = 102^\circ$
Solution: The values of $x$ and $y$ are: $x = 102^\circ$ $y = 78^\circ$