Geometry Unit 2: Angles, Lines and Triangle Congruence

Angles formed by parallel lines, triangle and polygon angle sums, the triangle inequality and congruence criteria. 12 questions. Have a go at each one on paper before you tap "Show me how".

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Question 1

Parallel linesNo calculator

A transversal crosses two parallel lines, making alternate interior angles of $(4x+6)^\circ$ and $(6x-28)^\circ$. Find $x$.

1. $74$
2. $106$
3. $17$
4. $20.2$

Question 2

Parallel linesNo calculator

Between two parallel lines, on the same side of a transversal, the two interior angles are $(2x+15)^\circ$ and $(4x-3)^\circ$. What is $x$?

1. $9$
2. $14$
3. $32$
4. $28$

Question 3

Triangle angle sumNo calculator

The angles of a triangle are in the ratio $1:2:3$. What is the largest angle, in degrees?

1. $90$
2. $60$
3. $30$
4. $120$

Question 4

Exterior anglesNo calculator

In triangle $ABC$, the exterior angle at $C$ measures $128^\circ$ and $m\angle A=55^\circ$. What is $m\angle B$?

1. $107$
2. $128$
3. $73$
4. $52$

Question 5

Isosceles trianglesNo calculator

The vertex angle of an isosceles triangle is $40^\circ$. What is each base angle?

1. $40$
2. $140$
3. $50$
4. $70$

Question 6

Polygon anglesNo calculator

What is the sum of the interior angles of a hexagon, in degrees?

1. $540$
2. $1080$
3. $360$
4. $720$

Question 7

Polygon anglesNo calculator

What is the measure of each interior angle of a regular decagon, in degrees?

1. $36$
2. $144$
3. $150$
4. $162$

Question 8

Congruence criteriaNo calculator

In triangles $ABC$ and $DEF$, $AB=DE$, $\angle B\cong\angle E$ and $BC=EF$. Which criterion proves the triangles congruent?

1. AAS
2. SAS
3. SSA
4. ASA

Question 9

Vertical anglesNo calculator

Two lines intersect. One angle measures $(7x-12)^\circ$ and the angle vertical to it measures $(4x+15)^\circ$. What is the measure of each of the other two angles?

1. $51$
2. $129$
3. $39$
4. $9$

Question 10

Triangle inequalityNo calculator

Two sides of a triangle are 7 and 12. Which could be the length of the third side?

1. $5$
2. $19$
3. $20$
4. $10$

Question 11

Angle bisectorsNo calculator

Ray $BD$ bisects $\angle ABC$. If $m\angle ABD=(3x+4)^\circ$ and $m\angle ABC=(8x-12)^\circ$, what is $m\angle ABC$?

1. $10$
2. $34$
3. $68$
4. $76$

Question 12

Congruent figuresNo calculator

Triangle $PQR\cong$ triangle $XYZ$. If $PQ=2a+3$ and $XY=5a-9$, how long is $PQ$?

1. $22$
2. $11$
3. $4$
4. $13$