Question

The measure of two angles of a triangle are $105°$ and $20°55‵$. Find the measure of the third angle.

Answer 1

The measure of two angles of a triangle are $105°$ and $20°55‵$.

Step I: Converting minutes into degrees.

We know, decimal degrees$=degrees+\frac{minutes}{60}$

$20°55‵$into degrees can be done by,

To convert $55‵$ into degrees, we have to divide it by $60$

Then add the result to $20°$.

$20°55\text{'}=20°+\frac{55\text{'}}{60}$

$=20°+0.9166°$

$=20.9166°$

Step II: Find the third angle of a triangle.

Let the measure of the third angle of a triangle be $x$.

The measure of two angles of a triangle are $105°$ and $20.9166°$.

By angle sum property,

The sum of angles of a triangle is $180°$.

$105°+20.9166°+\angle x=180°$

$125.9166°+\angle x=180°$

$\angle x=180°-125.9166°$

$\angle x=54.0834°$

Therefore, the measure of the third angle is $54.0834°$