Grade 7 Angles and Geometric Constructions Practice Test

Correct answer: A

The correct answer is $65^\circ$.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: Corresponding angles formed by parallel lines are congruent, so the measure is $65^\circ$.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: B

The correct answer is $70^\circ$.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: Subtract from $180^\circ$: $180^\circ-110^\circ=70^\circ$.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: C

The correct answer is $48^\circ$.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: Alternate interior angles are congruent when lines are parallel, so the measure is $48^\circ$.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: D

The correct answer is $55^\circ$.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: A linear pair sums to $180^\circ$: $180^\circ-125^\circ=55^\circ$.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: A

The correct answer is $15$.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: Set corresponding angles equal: $3x+5=50$. Then $3x=45$ and $x=15$.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: B

The correct answer is $30$.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: Set the congruent angles equal: $2x+10=70$. Thus $x=30$.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: C

The correct answer is $30$.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: They are supplementary: $4x+2x=180$. Thus $6x=180$ and $x=30$.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: D

The correct answer is $30$.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: Set them equal: $x+20=3x-40$. Solving gives $2x=60$, so $x=30$.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: A

The correct answer is $36$.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: Set the sum to $180^\circ$: $3x-15+2x+15=180$. Thus $5x=180$ and $x=36$.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.

Correct answer: B

The correct answer is $30$.

1. Identify the angle relationship or construction: Determine whether the problem uses complementary, supplementary, vertical, parallel-line, or construction properties.
2. Apply the geometry rule: Set the congruent angles equal: $x+25=2x-5$. Therefore, $x=30$.
3. Check the result: Verify the angle measure, equality, or construction step using the defining property.