Triangle angle sum. Game on.

Triangle angle sum is a grade 8 math skill aligned to Common Core standard 8.G.A.5: use informal arguments to establish facts about the angle sum and exterior angle of triangles, and about the angles created when parallel lines are cut by a transversal. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 triangle angle sum problems our math games drill.

CCSS 8.G.A.510 questions in the bank
Kickoff

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Warm-upeasy

In a triangle, m∠P=105∘m\angle P = 105^{\circ} and m∠Q=28∘.m\angle Q = 28^{\circ}\textsf{.} What is m∠R?m\angle R\textsf{?}

The sum of the interior angles of a triangle is 180∘.180^{\circ}\textsf{.} So m∠R=180∘−105∘−28∘=47∘.m\angle R = 180^{\circ} - 105^{\circ} - 28^{\circ} = 47^{\circ}\textsf{.}

Mid-gameeasy

The measures of two angles of a triangle are 37∘37^{\circ} and 84∘.84^{\circ}\textsf{.} What is the measure of the remaining angle?

The sum of the interior angles of a triangle is 180∘.180^{\circ}\textsf{.} The remaining angle measures 180∘−37∘−84∘=59∘.180^{\circ} - 37^{\circ} - 84^{\circ} = 59^{\circ}\textsf{.}

Mid-gameeasy

A right triangle has an acute angle that measures 22∘.22^{\circ}\textsf{.} What is the measure of the other acute angle?

The right angle measures 90∘,90^{\circ}\textsf{,} and the sum of the interior angles of a triangle is 180∘.180^{\circ}\textsf{.} The other acute angle measures 180∘−90∘−22∘=68∘.180^{\circ} - 90^{\circ} - 22^{\circ} = 68^{\circ}\textsf{.}

Mid-gameeasy

In △DEF,\triangle DEF\textsf{,} m∠Dm\angle D and m∠Em\angle E together measure 127∘.127^{\circ}\textsf{.} What is m∠F?m\angle F\textsf{?}

The sum of the interior angles of a triangle is 180∘.180^{\circ}\textsf{.} So m∠F=180∘−127∘=53∘.m\angle F = 180^{\circ} - 127^{\circ} = 53^{\circ}\textsf{.}

Mid-gameeasy

A triangle has angle measures 41∘,41^{\circ}\textsf{,} 96∘,96^{\circ}\textsf{,} and n∘.n^{\circ}\textsf{.} What is the value of n?n\textsf{?}

The sum of the interior angles of a triangle is 180∘.180^{\circ}\textsf{.} So n∘=180∘−41∘−96∘,n^{\circ} = 180^{\circ} - 41^{\circ} - 96^{\circ}\textsf{,} and n=43.n = 43\textsf{.}

Mid-gameeasy

If m∠A=50∘m\angle A = 50^{\circ} and m∠B=78∘m\angle B = 78^{\circ} in a triangle, what is m∠C?m\angle C\textsf{?}

The sum of the interior angles of a triangle is 180∘.180^{\circ}\textsf{.} So m∠C=180∘−50∘−78∘=52∘.m\angle C = 180^{\circ} - 50^{\circ} - 78^{\circ} = 52^{\circ}\textsf{.}

Mid-gameeasy

The angles of a triangle measure 33∘,33^{\circ}\textsf{,} 88∘,88^{\circ}\textsf{,} and k∘.k^{\circ}\textsf{.} What is the value of k?k\textsf{?}

The sum of the interior angles of a triangle is 180∘.180^{\circ}\textsf{.} So k∘=180∘−33∘−88∘,k^{\circ} = 180^{\circ} - 33^{\circ} - 88^{\circ}\textsf{,} and k=59.k = 59\textsf{.}

Buzzer beatereasy

In △MNP,\triangle MNP\textsf{,} m∠M=64∘m\angle M = 64^{\circ} and m∠N=64∘.m\angle N = 64^{\circ}\textsf{.} What is m∠P?m\angle P\textsf{?}

The sum of the interior angles of a triangle is 180∘.180^{\circ}\textsf{.} So m∠P=180∘−64∘−64∘=52∘.m\angle P = 180^{\circ} - 64^{\circ} - 64^{\circ} = 52^{\circ}\textsf{.}

Overtime

2 more. Played, not assigned.

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Tests that cover triangle angle sum:
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