Introduction

A triangle has three sides and three interior angles. Teachers often ask students to find an unknown angle. Two reliable methods are:

1. The 180° rule: the sum of all interior angles is always 180°.
2. The Law of Sines: sin A / a = sin B / b, where A and B are angles and a and b are the sides opposite them.

When Two Angles Are Known

Step 1

Sum the two known angles.

Step 2

Subtract that sum from 180° to get the missing angle.

Step 3

Express the result in degrees.

When One Angle and Two Opposite Sides Are Known (SSA)

Step 1

Set up the Law of Sines: sin A / a = sin B / b.

Step 2

Plug in the known values. For example, if angle A = 25° with opposite side a = 7, and side b = 12 opposite the unknown angle B, the equation becomes sin B / 12 = sin 25° / 7.

Step 3

Rearrange to solve for sin B: sin B = (sin 25° × 12) / 7.

Step 4

Compute sin 25° (≈ 0.4226). Then sin B ≈ 0.724.

Step 5

Find the inverse sine: B ≈ 46°.

Step 6

Check whether the angle could be obtuse. The calculator returns only the acute solution; an obtuse solution would satisfy 180° – 46° = 134°. Use a protractor or context clues to decide which is correct.

Step 7

Once B is determined, compute the remaining angle using the 180° rule.

Tools You’ll Need

• Scientific calculator
• Protractor

TL;DR

Equilateral triangles always have 60° angles. Otherwise, use the 180° rule or the Law of Sines to find missing angles.