We are given two angles of the triangle: one is 50^° and the other is 30^°. We need to find the measure of the third angle.

First, add the two known angles: 50^° + 30^° = 80^°. Then, subtract this sum from 180^° to find the measure of the third angle. This gives us 180^° - 80^° = 100^°.

Two angles of a triangle are 50 and 30. What is the third?

Answer: The third angle of the triangle is $100^\circ$ .

Step-by-step solution

Step 1: Recall Angle Sum Property

The fundamental property of any triangle states that the sum of its three interior angles is always equal to $180^\circ$ . This is a key concept in geometry.

Step 2: Identify Given Angles

We are given two angles of the triangle: one is $50^\circ$ and the other is $30^\circ$ . We need to find the measure of the third angle.

Step 3: Set Up Equation

Let the third angle be $x$ . According to the angle sum property, we can set up an equation where the sum of the two given angles and the unknown third angle equals $180^\circ$ .

Step 4: Solve for the Third Angle

First, add the two known angles: $50^\circ + 30^\circ = 80^\circ$ . Then, subtract this sum from $180^\circ$ to find the measure of the third angle. This gives us $180^\circ - 80^\circ = 100^\circ$ .

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