Question

the measures of two angles of a triangle are given. find the measure of the third angle. 28° 2, 138° 21 the measure of the third angle is □°□. (simplify your answer. type a whole number.)

Explanation:

Step1: Convert degrees and minutes to minutes

We know that $1^{\circ}=60'$. So $28^{\circ}2'=(28\times60 + 2)'=1682'$ and $138^{\circ}21'=(138\times60+21)' = 8301'$. The sum of angles in a triangle is $180^{\circ}=180\times60' = 10800'$.

Step2: Calculate the third - angle in minutes

Let the third - angle be $x$ minutes. Then $x=10800-(1682 + 8301)$.
$x=10800 - 9983=817'$.

Step3: Convert back to degrees and minutes

Divide 817 by 60. The quotient is the degree part and the remainder is the minute part. $817\div60 = 13\cdots\cdots37$. So $817'=13^{\circ}37'$.

Answer:

$13^{\circ}37'$