L3 · Angle relationships in triangles

Learning goal

“I can justify an unknown interior angle of a triangle using the theorems in 8G2: the interior angles sum to 180 degrees; in an isosceles triangle, the angles opposite the equal sides are equal; and every angle of an equilateral triangle is 60 degrees.”

Interior angle — an angle inside a triangle at one of its vertices. A triangle has exactly three interior angles.

Isosceles triangle — a triangle with two equal sides - picture two sides marked with matching tick marks.

Base angles — in an isosceles triangle, the two angles opposite the two equal sides. The base angles are always equal to each other. ("Base angles" names a relationship, not a position - they need not sit at the bottom of the page.)

Equilateral triangle — a triangle with all three sides equal. All three of its interior angles are 60 degrees.

Worked example

Two interior angles of a triangle measure 47 degrees and 63 degrees. Find the third, and justify it. Step 1: Name the theorem: the interior angles of a triangle sum to 180 degrees. Step 2: 47 + 63 = 110. Step 3: 180 - 110 = 70 degrees. The third angle is 70 degrees - justified BY the theorem, not by how the drawing looks.

Check yourself — explain it

A triangle has angles 90 degrees and 41 degrees. The third angle is 49 degrees because...

Paired problem — example still visible

Angles 88 degrees and 35 degrees -> third = 180 - 123 = 57 degrees

Faded completion — last step is yours

"A right triangle has one acute angle of 41 degrees. The other acute angle: 180 - 90 - ___ = ___" -> 41; 49 degrees

Ready to practise?

10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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