Question

The measures of two angles of a triangle are $22\mathrm{and}85$ degrees. Find the measure of the third angle.

Short answer

The measure of the third angle is$73°.$

Step-by-step solution

Step 1. Given Information   

The measure of two angles are$22\mathrm{and}85$and we have to find the measure of the third angle.

Step 2. Translate into an equation

Let xbe the measure of the third angle.

The sum of the angle of a triangle is $180°.$

So, the equation isrole="math" localid="1647264130553" $22°+85°+x=180°$

Step 3. Solve the equation

By proceeding with the equation we get,

$$\begin{gathered} 22°+85°+x=180° \\ 105°+x=180° \\ x=180°-107° \\ x=73° \end{gathered}$$

Thus, the measure of the third angle is$73$degree.

Step 4. Check the answer

To check the answer substitute the angle $73$in the formula of the sum of a triangle.

$$\begin{gathered} 22°+85°+73°=180° \\ 180°=180° \end{gathered}$$

It is true.

Thus, the measure of the third angle is $73°.$$$\begin{gathered} 22°+85°+73°=180° \\ 180°=180° \end{gathered}$$