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Angles in a Triangle: Practice

12 multiple-choice questions, progressively harder.

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

In triangle $ABC$ , point $D$ is between $A$ and $B$ . Given $m\angle CAB=33^\circ$ , $m\angle ABC=59^\circ$ , and $m\angle ACD=41^\circ$ , find $m\angle DCB$ .

Answer choices for question 1 A $88^\circ$ B $106^\circ$ C $74^\circ$ D $47^\circ$
2

In triangle $ABC$ , $D$ lies inside side $AB$ , $E$ lies inside side $AC$ , and $DE\parallel BC$ . The angles at $A,B$ measure $57^\circ,48^\circ$ . Find $m\angle AED$ .

Answer choices for question 2 A $57^\circ$ B $75^\circ$ C $48^\circ$ D $105^\circ$
3

A triangle has angle measures $(2x+1)^\circ$ , $(4x-3)^\circ$ , and $(5x+6)^\circ$ . Which describes the triangle after solving for $x$ ?

Answer choices for question 3 A Acute, with largest angle 86 degrees B Obtuse, with an angle of 96 degrees C Right, with an angle of 90 degrees D Acute, with largest angle 79 degrees
4

The acute angles of a right triangle differ by $26^\circ$ . Find the larger one.

Answer choices for question 4 A $32^\circ$ B $77^\circ$ C $58^\circ$ D $64^\circ$
5

Two angles of a nondegenerate triangle are complementary. Which argument establishes its angle classification?

Answer choices for question 5 A They are both acute, so the triangle must be acute B Their sum is 90 degrees, so the third is 180 minus 90 degrees and the triangle is right C Their sum is 180 degrees, so the third is a right angle D Complementary angles must be congruent, so the triangle is equilateral
6

In the triangle angle-sum construction, $D,C,E$ are collinear in that order, $DE\parallel AB$ , and the triangle is below $DE$ as shown. Which two angle congruences follow by alternate interior angles?

Answer choices for question 6 A $\angle DCA\cong\angle CAB$ and $\angle BCE\cong\angle ABC$ B $\angle DCA\cong\angle ABC$ and $\angle BCE\cong\angle CAB$ C $\angle DCA\cong\angle ACB$ and $\angle BCE\cong\angle ACB$ D $\angle CAB\cong\angle ABC$ and $\angle DCA\cong\angle BCE$
7

Triangle $ABC$ is right at $B$ . Point $D$ lies inside side $AC$ , and $BD\perp AC$ . If $m\angle BAC=28^\circ$ , find $m\angle DBC$ .

Answer choices for question 7 A $62^\circ$ B $90^\circ$ C $34^\circ$ D $28^\circ$
8

In triangle $ABC$ , $D$ lies between $B$ and $C$ , and $AD$ bisects $\angle BAC$ . The angles at $B,C$ measure $58^\circ,66^\circ$ . Find $m\angle ADC$ .

Answer choices for question 8 A $56^\circ$ B $28^\circ$ C $86^\circ$ D $94^\circ$
9

Two distinct lines contain $A,O,C$ in that order and $B,O,D$ in that order. In triangle $AOB$ , the angles at $A,B$ measure $(2x+3)^\circ,(3x+7)^\circ$ . In triangle $COD$ , the angles at $C,D$ measure $44^\circ,56^\circ$ . Find $m\angle OAB$ .

Answer choices for question 9 A $39^\circ$ B $18^\circ$ C $61^\circ$ D $80^\circ$
10

Two interior angles of a triangle are proposed as $(2u+4)^\circ$ and $(u+8)^\circ$ . Which value of $u$ gives two positive measures whose sum leaves a positive third angle?

Answer choices for question 10 A $-5$ B $-3$ C $57$ D $55$
11

Triangles $ABC$ and $PQR$ satisfy $\angle A\cong\angle Q$ and $\angle B\cong\angle R$ . Which remaining correspondence follows?

Answer choices for question 11 A $\angle C\cong\angle Q$ B $\angle C\cong\angle P$ C $\angle A\cong\angle P$ D $\angle B\cong\angle P$
12

In triangle $KLM$ , $N$ lies between $K$ and $L$ . Given $m\angle LKM=36^\circ$ , $m\angle KLM=72^\circ$ , and $m\angle KMN=24^\circ$ , which sequence correctly finds $m\angle NML$ through the smaller triangles?

Answer choices for question 12 A Find angle KNM as 60 degrees, angle MNL as 120 degrees, then angle NML as negative 12 degrees B Find angle KNM as 120 degrees, angle MNL as 120 degrees, then angle NML as negative 12 degrees C Find angle KNM as 120 degrees, angle MNL as 60 degrees, then angle NML as 48 degrees D Find angle KNM as 156 degrees, angle MNL as 24 degrees, then angle NML as 84 degrees

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