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PEAZIT Aha card

Three triangle angles make a straight angle

In plane geometry, a triangle's interior angles total 180°. Subtract the known angles from this total.

Angles of 50° and 60° leave 70°.

Relation	Meaning
α + β + γ = 180°	The complete total is 180°.
γ = 180° − 50° − 60°	Subtract both known angles.
γ = 70°	Check: 50 + 60 + 70 = 180.

One worked example

α + β + γ = 180°The complete total is 180°.
γ = 180° − 50° − 60°Subtract both known angles.
γ = 70°Check: 50 + 60 + 70 = 180.

Watch out: This rule describes a triangle in a plane. Do not confuse exterior and interior angles.

Goal, prerequisites and card origin

What you will learn: Find the missing interior angle.

What you need first: Degrees and straight angles.

An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1

Show connections

In plane geometry, a triangle's interior angles total 180°. Subtract the known angles from this total.

Without JavaScript, write your answer elsewhere before opening the solution.Two interior angles are 45° and 80°. How many degrees is the third? Enter a number.

Solution — open after your own attempt

55 180 − 45 − 80 = 55°.

A question for your next return: An isosceles triangle has two base angles of 70°. How many degrees is its vertex angle?

Solution — open after your own attempt

40 180 − 70 − 70 = 40°.

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