Math / Geometry

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

Studdy Solution

STEP 1

1. The given angles are part of an intersecting line pair, forming vertical angles and linear pairs.
2. Vertical angles are equal in measure.
3. The sum of angles on a straight line (linear pair) is $180^\circ$ .
4. The angles labeled as $y$ are adjacent to the $120^\circ$ angle.

STEP 2

1. Determine the value of $x$ using the property of vertical angles.
2. Determine the value of $y$ using the property of linear pairs.

STEP 3

Since vertical angles are equal, set $x$ equal to the given vertical angle of $120^\circ$ . $x = 120^\circ$

STEP 4

Angles on a straight line sum to $180^\circ$ . Therefore, the angle adjacent to the $120^\circ$ angle, which is labeled $y$ , can be found as: $y = 180^\circ - 120^\circ$

STEP 5

Perform the subtraction to find $y$ . $y = 60^\circ$
Solution: The values of the angles are: $x = 120^\circ$ $y = 60^\circ$

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

Studdy Solution

STEP 1

1. The given angles are part of an intersecting line pair, forming vertical angles and linear pairs.
2. Vertical angles are equal in measure.
3. The sum of angles on a straight line (linear pair) is $180^\circ$ .
4. The angles labeled as $y$ are adjacent to the $120^\circ$ angle.

STEP 2

1. Determine the value of $x$ using the property of vertical angles.
2. Determine the value of $y$ using the property of linear pairs.

STEP 3

Since vertical angles are equal, set $x$ equal to the given vertical angle of $120^\circ$ . $x = 120^\circ$

STEP 4

Angles on a straight line sum to $180^\circ$ . Therefore, the angle adjacent to the $120^\circ$ angle, which is labeled $y$ , can be found as: $y = 180^\circ - 120^\circ$

STEP 5

Perform the subtraction to find $y$ . $y = 60^\circ$
Solution: The values of the angles are: $x = 120^\circ$ $y = 60^\circ$

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QuestionFind the values of xxx and yyy.

Studdy Solution

STEP 1

1. The given angles are part of an intersecting line pair, forming vertical angles and linear pairs.2. Vertical angles are equal in measure.3. The sum of angles on a straight line (linear pair) is 180∘180^\circ180∘.4. The angles labeled as yyy are adjacent to the 120∘120^\circ120∘ angle.

STEP 2

1. Determine the value of xxx using the property of vertical angles.2. Determine the value of yyy using the property of linear pairs.

STEP 3

Since vertical angles are equal, set xxx equal to the given vertical angle of 120∘120^\circ120∘. x=120∘ x = 120^\circ x=120∘

STEP 4

Angles on a straight line sum to 180∘180^\circ180∘. Therefore, the angle adjacent to the 120∘120^\circ120∘ angle, which is labeled yyy, can be found as: y=180∘−120∘ y = 180^\circ - 120^\circ y=180∘−120∘

STEP 5

Perform the subtraction to find yyy. y=60∘ y = 60^\circ y=60∘Solution: The values of the angles are: x=120∘ x = 120^\circ x=120∘ y=60∘ y = 60^\circ y=60∘

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

1. The given angles are part of an intersecting line pair, forming vertical angles and linear pairs.
2. Vertical angles are equal in measure.
3. The sum of angles on a straight line (linear pair) is $180^\circ$ .
4. The angles labeled as $y$ are adjacent to the $120^\circ$ angle.

1. Determine the value of $x$ using the property of vertical angles.
2. Determine the value of $y$ using the property of linear pairs.

Since vertical angles are equal, set $x$ equal to the given vertical angle of $120^\circ$ . $x = 120^\circ$

Angles on a straight line sum to $180^\circ$ . Therefore, the angle adjacent to the $120^\circ$ angle, which is labeled $y$ , can be found as: $y = 180^\circ - 120^\circ$

Perform the subtraction to find $y$ . $y = 60^\circ$
Solution: The values of the angles are: $x = 120^\circ$ $y = 60^\circ$