Question

the measures of two angles of a triangle are given. find the measure of the third angle. 38° 59, 124° 14 the measure of the third angle is ° . (simplify your answer. type a whole number.)

Explanation:

Step1: Recall angle - sum property of triangle

The sum of the interior angles of a triangle is $180^{\circ}= 179^{\circ}60'$.

Step2: Add the given angles

$38^{\circ}59'+124^{\circ}14'=(38 + 124)^{\circ}+(59 + 14)'=162^{\circ}73'$. Since $73'=60'+13' = 1^{\circ}13'$, the sum is $163^{\circ}13'$.

Step3: Find the third - angle

Subtract the sum of the two given angles from $180^{\circ}(179^{\circ}60')$. $179^{\circ}60'-163^{\circ}13'=(179 - 163)^{\circ}+(60 - 13)'=16^{\circ}47'$.

Answer:

$16^{\circ}47'$