Math / Geometry

QuestionFind the measure of $\measuredangle 6$ . $\triangle 6=[?]^{\circ}$

Studdy Solution

STEP 1

1. The sum of angles around a point is $360^\circ$ .
2. Vertical angles (angles opposite each other when two lines intersect) are equal.
3. Adjacent angles on a straight line sum to $180^\circ$ .

STEP 2

1. Identify the relationships between the given angles.
2. Use angle relationships to find $\angle 6$ .

STEP 3

Identify the relationships between the given angles. Since the lines intersect, we have pairs of vertical angles and linear pairs.

STEP 4

Since $\angle 6$ is vertically opposite to the angle marked $78^\circ$ , we can use the property of vertical angles.

STEP 5

Vertical angles are equal, so:
$\measuredangle 6 = 78^\circ$
The measure of $\measuredangle 6$ is:
$\boxed{78^\circ}$

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QuestionFind the measure of $\measuredangle 6$ . $\triangle 6=[?]^{\circ}$

Studdy Solution

STEP 1

1. The sum of angles around a point is $360^\circ$ .
2. Vertical angles (angles opposite each other when two lines intersect) are equal.
3. Adjacent angles on a straight line sum to $180^\circ$ .

STEP 2

1. Identify the relationships between the given angles.
2. Use angle relationships to find $\angle 6$ .

STEP 3

Identify the relationships between the given angles. Since the lines intersect, we have pairs of vertical angles and linear pairs.

STEP 4

Since $\angle 6$ is vertically opposite to the angle marked $78^\circ$ , we can use the property of vertical angles.

STEP 5

Vertical angles are equal, so:
$\measuredangle 6 = 78^\circ$
The measure of $\measuredangle 6$ is:
$\boxed{78^\circ}$

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QuestionFind the measure of ∡6\measuredangle 6∡6. △6=[?]∘\triangle 6=[?]^{\circ}△6=[?]∘

Studdy Solution

STEP 1

1. The sum of angles around a point is 360∘360^\circ360∘.2. Vertical angles (angles opposite each other when two lines intersect) are equal.3. Adjacent angles on a straight line sum to 180∘180^\circ180∘.

STEP 2

1. Identify the relationships between the given angles.2. Use angle relationships to find ∠6\angle 6∠6.

STEP 3

Identify the relationships between the given angles. Since the lines intersect, we have pairs of vertical angles and linear pairs.

STEP 4

Since ∠6\angle 6∠6 is vertically opposite to the angle marked 78∘78^\circ78∘, we can use the property of vertical angles.

STEP 5

Vertical angles are equal, so:∡6=78∘\measuredangle 6 = 78^\circ∡6=78∘ The measure of ∡6\measuredangle 6∡6 is:78∘\boxed{78^\circ}78∘​

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QuestionFind the measure of $\measuredangle 6$ . $\triangle 6=[?]^{\circ}$

1. The sum of angles around a point is $360^\circ$ .
2. Vertical angles (angles opposite each other when two lines intersect) are equal.
3. Adjacent angles on a straight line sum to $180^\circ$ .

1. Identify the relationships between the given angles.
2. Use angle relationships to find $\angle 6$ .

Since $\angle 6$ is vertically opposite to the angle marked $78^\circ$ , we can use the property of vertical angles.

Vertical angles are equal, so:
$\measuredangle 6 = 78^\circ$
The measure of $\measuredangle 6$ is:
$\boxed{78^\circ}$