Level 2 · Intermediate ← Back to lesson

The Exterior Angle Theorem: Practice

12 multiple-choice questions, progressively harder.

Level 2 · Intermediate 0 / 12 answered

Question 1 of 12

1

Triangle $ABC$ has $BC$ extended beyond $C$ to $D$ , with $B,C,D$ in that order. The measures in degrees are $m\angle BAC=5x-2$ , $m\angle ABC=2x+9$ , and $m\angle ACD=10x-17$ . What is $x$ ?

Answer choices for question 1 A $6$ B $8$ C $12$ D $28$
2

The two remote interior angles for a triangle's $119^\circ$ exterior angle have measures in the ratio $2:5$ . What are those two measures?

Answer choices for question 2 A $17^\circ$ and $102^\circ$ B $24^\circ$ and $60^\circ$ C $47.6^\circ$ and $71.4^\circ$ D $34^\circ$ and $85^\circ$
3

One non-reflex exterior angle at vertex $A$ of triangle $ABC$ measures $148^\circ$ , and one at $B$ measures $107^\circ$ . What is a non-reflex exterior angle measure at $C$ ?

Answer choices for question 3 A $105^\circ$ B $75^\circ$ C $41^\circ$ D $255^\circ$
4

Triangle $ABC$ has $BC$ extended beyond $C$ to $D$ , with $B,C,D$ in that order. If $m\angle ACD=121^\circ$ , $m\angle BAC=(3x+7)^\circ$ , and $m\angle ABC=(x+10)^\circ$ , what is $m\angle BAC$ ?

Answer choices for question 4 A $26^\circ$ B $36^\circ$ C $85^\circ$ D $59^\circ$
5

A measurement record for a triangle gives an exterior angle of $87^\circ$ and one of its remote interior angles as $92^\circ$ . Which conclusion follows?

Answer choices for question 5 A The other remote angle is $5^\circ$ B The adjacent interior angle is $92^\circ$ C The record is valid because both angles are below $180^\circ$ D The record is inconsistent because a remote angle cannot exceed its exterior angle
6

At a triangle vertex, a non-reflex exterior angle has three times the measure of its adjacent interior angle. What is the exterior measure?

Answer choices for question 6 A $45^\circ$ B $135^\circ$ C $60^\circ$ D $120^\circ$
7

Triangle $ABC$ has $BC$ extended beyond $C$ to $D$ , with $B,C,D$ in that order. The remote interior angles at $A$ and $B$ measure $54^\circ$ and $62^\circ$ . Ray $CE$ lies strictly inside $\angle ACD$ , and $m\angle ECD=39^\circ$ . What is $m\angle ACE$ ?

Answer choices for question 7 A $116^\circ$ B $103^\circ$ C $77^\circ$ D $155^\circ$
8

A path follows a triangle once, with all three non-reflex exterior turns to the right. Their degree measures are $x+65$ , $2x+30$ , and $3x-5$ . What is $x$ ?

Answer choices for question 8 A $45$ B $15$ C $30$ D $60$
9

A path follows triangle $ABC$ once, taking one non-reflex left exterior turn at each vertex. Its interior measures are $a,b,c$ , and the corresponding exterior turn measures are $e_A,e_B,e_C$ . Which step justifies a total exterior turn of $360^\circ$ ?

Answer choices for question 9 A Use $e_A=a$ , $e_B=b$ , and $e_C=c$ , since adjacent angles are supplementary B Add the three linear-pair equations and substitute $a+b+c=180^\circ$ C Use $e_A+e_B+e_C=180^\circ$ , because all the angles belong to a triangle D Conclude $e_A=e_B=e_C$ from the exterior angle inequality
10

In triangle $ABC$ , extend $BC$ beyond $C$ to $D$ and extend $AC$ beyond $C$ to $E$ . Thus $B,C,D$ and $A,C,E$ are each in the stated order on distinct lines. If $m\angle ACB=72^\circ$ , what is $m\angle BCE$ ?

Answer choices for question 10 A $72^\circ$ B $36^\circ$ C $108^\circ$ D $144^\circ$
11

A triangle has an exterior angle of $104^\circ$ . One remote interior angle has measure $a$ , and the other has measure $2a+8^\circ$ . What is the second remote measure?

Answer choices for question 11 A $72^\circ$ B $32^\circ$ C $76^\circ$ D $96^\circ$
12

A triangular path takes three non-reflex exterior turns, all to the left. Two measure $133^\circ$ and $102^\circ$ . What is the interior angle at the third vertex?

Answer choices for question 12 A $125^\circ$ B $78^\circ$ C $47^\circ$ D $55^\circ$

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