Angles in triangles — Mathematics, 11–13 years
The three inside angles of every triangle always add up to a straight angle. Mathematics, 11–13 years.
A triangle has a fixed total
Whatever its shape, a triangle has three inside angles whose measures add to 180°. A narrow, tall triangle and a wide, flat triangle may look very different, but opening one angle more forces the others to open less. The total stays the same.
Why this rule helps
When a diagram hides one angle, measuring it with a ruler is not enough, and guessing can be unreliable. The fixed total lets us find the missing angle from the two we can see. This works because the three corners of a triangle fit together to make a straight turn.
Finding the third angle
A triangle has angles of 48° and 67°. First add them: 48 + 67 = 115°. All three must total 180°, so subtract: 180 − 115 = 65°. The missing angle is 65°, which can be checked because 48 + 67 + 65 = 180°.
Trusting the drawing
It is tempting to call an angle 90° because it looks like a right angle, or to assume two sides are equal because the sketch looks balanced. Drawings are often not made to scale, so appearance is only a clue. Use the marked information and the 180° rule instead.
Strong shapes
Triangles are useful in bridges, roof frames and bicycle structures because their angles help keep the shape firm. A rectangle can wobble unless it has extra support, but a diagonal brace turns part of it into triangles. Builders calculate angles so pieces meet safely.
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