Math / Geometry

Question $m \angle x=0 u$
Prove: $m \angle 7=120^{\circ}$
Statements Reasons $m|\mid n$ $m \angle 2=60^{\circ}$ $\angle 8 \approx \angle 2$ $m \angle 8=m \angle 2$ 2 $m(8-60)$ Angle Congruence Postulate Substitution Property of Equality $m \angle 7+m \angle 8=180^{\circ}$ Linear Pair Postulate

Studdy Solution

STEP 1

1. We are given that $m \angle x = 0$ and need to prove $m \angle 7 = 120^\circ$ .
2. We have a list of statements and reasons to use in the proof.
3. We assume that the angles are part of a geometric figure where linear pairs and congruence can be applied.

STEP 2

1. Analyze the given statements and reasons.
2. Use the Angle Congruence Postulate.
3. Apply the Substitution Property of Equality.
4. Use the Linear Pair Postulate to find $m \angle 7$ .

STEP 3

Analyze the given statements and reasons to understand the relationships between the angles.
- $m \angle 2 = 60^\circ$ - $\angle 8 \approx \angle 2$ implies $m \angle 8 = m \angle 2$ by the Angle Congruence Postulate. - $m \angle 8 = 60^\circ$ by substitution.

STEP 4

Use the Angle Congruence Postulate to establish that $m \angle 8 = m \angle 2$ .
- Given $\angle 8 \approx \angle 2$ , we have $m \angle 8 = 60^\circ$ .

STEP 5

Apply the Substitution Property of Equality to substitute the known measures.
- Since $m \angle 8 = 60^\circ$ , substitute this value into any relevant equations.

STEP 6

Use the Linear Pair Postulate to find $m \angle 7$ .
- Given $m \angle 7 + m \angle 8 = 180^\circ$ , substitute $m \angle 8 = 60^\circ$ to find $m \angle 7$ .
$m \angle 7 + 60^\circ = 180^\circ$

STEP 7

Solve for $m \angle 7$ .
$m \angle 7 = 180^\circ - 60^\circ$ $m \angle 7 = 120^\circ$
The measure of $m \angle 7$ is $\boxed{120^\circ}$ .

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Question $m \angle x=0 u$
Prove: $m \angle 7=120^{\circ}$
Statements Reasons $m|\mid n$ $m \angle 2=60^{\circ}$ $\angle 8 \approx \angle 2$ $m \angle 8=m \angle 2$ 2 $m(8-60)$ Angle Congruence Postulate Substitution Property of Equality $m \angle 7+m \angle 8=180^{\circ}$ Linear Pair Postulate

Studdy Solution

STEP 1

1. We are given that $m \angle x = 0$ and need to prove $m \angle 7 = 120^\circ$ .
2. We have a list of statements and reasons to use in the proof.
3. We assume that the angles are part of a geometric figure where linear pairs and congruence can be applied.

STEP 2

1. Analyze the given statements and reasons.
2. Use the Angle Congruence Postulate.
3. Apply the Substitution Property of Equality.
4. Use the Linear Pair Postulate to find $m \angle 7$ .

STEP 3

Analyze the given statements and reasons to understand the relationships between the angles.
- $m \angle 2 = 60^\circ$ - $\angle 8 \approx \angle 2$ implies $m \angle 8 = m \angle 2$ by the Angle Congruence Postulate. - $m \angle 8 = 60^\circ$ by substitution.

STEP 4

Use the Angle Congruence Postulate to establish that $m \angle 8 = m \angle 2$ .
- Given $\angle 8 \approx \angle 2$ , we have $m \angle 8 = 60^\circ$ .

STEP 5

Apply the Substitution Property of Equality to substitute the known measures.
- Since $m \angle 8 = 60^\circ$ , substitute this value into any relevant equations.

STEP 6

Use the Linear Pair Postulate to find $m \angle 7$ .
- Given $m \angle 7 + m \angle 8 = 180^\circ$ , substitute $m \angle 8 = 60^\circ$ to find $m \angle 7$ .
$m \angle 7 + 60^\circ = 180^\circ$

STEP 7

Solve for $m \angle 7$ .
$m \angle 7 = 180^\circ - 60^\circ$ $m \angle 7 = 120^\circ$
The measure of $m \angle 7$ is $\boxed{120^\circ}$ .

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Studdy Solution

STEP 1

1. We are given that m∠x=0 m \angle x = 0 m∠x=0 and need to prove m∠7=120∘ m \angle 7 = 120^\circ m∠7=120∘.2. We have a list of statements and reasons to use in the proof.3. We assume that the angles are part of a geometric figure where linear pairs and congruence can be applied.

STEP 2

1. Analyze the given statements and reasons.2. Use the Angle Congruence Postulate.3. Apply the Substitution Property of Equality.4. Use the Linear Pair Postulate to find m∠7 m \angle 7 m∠7.

STEP 3

STEP 4

Use the Angle Congruence Postulate to establish that m∠8=m∠2 m \angle 8 = m \angle 2 m∠8=m∠2.- Given ∠8≈∠2 \angle 8 \approx \angle 2 ∠8≈∠2, we have m∠8=60∘ m \angle 8 = 60^\circ m∠8=60∘.

STEP 5

Apply the Substitution Property of Equality to substitute the known measures.- Since m∠8=60∘ m \angle 8 = 60^\circ m∠8=60∘, substitute this value into any relevant equations.

STEP 6

STEP 7

Solve for m∠7 m \angle 7 m∠7.m∠7=180∘−60∘ m \angle 7 = 180^\circ - 60^\circ m∠7=180∘−60∘ m∠7=120∘ m \angle 7 = 120^\circ m∠7=120∘ The measure of m∠7 m \angle 7 m∠7 is 120∘ \boxed{120^\circ} 120∘​.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. We are given that $m \angle x = 0$ and need to prove $m \angle 7 = 120^\circ$ .
2. We have a list of statements and reasons to use in the proof.
3. We assume that the angles are part of a geometric figure where linear pairs and congruence can be applied.

1. Analyze the given statements and reasons.
2. Use the Angle Congruence Postulate.
3. Apply the Substitution Property of Equality.
4. Use the Linear Pair Postulate to find $m \angle 7$ .

Use the Angle Congruence Postulate to establish that $m \angle 8 = m \angle 2$ .
- Given $\angle 8 \approx \angle 2$ , we have $m \angle 8 = 60^\circ$ .

Apply the Substitution Property of Equality to substitute the known measures.
- Since $m \angle 8 = 60^\circ$ , substitute this value into any relevant equations.

Solve for $m \angle 7$ .
$m \angle 7 = 180^\circ - 60^\circ$ $m \angle 7 = 120^\circ$
The measure of $m \angle 7$ is $\boxed{120^\circ}$ .