Questions: In the diagram of triangle JEA below, m angle JEA=90 and m angle EAJ=48. Line segment MS connects points M and S on the triangle, such that m angle EMS=59. What is m angle JSM?

In the diagram of triangle JEA below, m angle JEA=90 and m angle EAJ=48. Line segment MS connects points M and S on the triangle, such that m angle EMS=59.

What is m angle JSM?

Transcript text: In the diagram of $\triangle J E A$ below, $\mathrm{m} \angle J E A=90$ and $\mathrm{m} \angle E . A J=48$ : Line segment $M S$ connects points $M$ and $S$ on the triangle, such that $\mathrm{m} \angle E M S=59$. What is $\mathrm{m} \angle J S M$ ?

Solution

Solution Steps

Step 1: Find the measure of angle JAE.

The sum of the angles in a triangle is 180 degrees. In triangle JEA, we have a right angle at E (90 degrees) and angle EAJ is 48 degrees. Therefore, angle AJE is 180 - 90 - 48 = 42 degrees.

Step 2: Find the measure of angle JMS.

Triangle JME also has angle JEM equal to 90 degrees and angle EJM equal to 59 degrees. Therefore angle JMS = 180 - 90- 59 = 31 degrees.

Step 3: Find the measure of angle JSM.

The sum of angles in triangle JMS is 180 degrees. We know angle MJS is 42 degrees (from step 1) and angle JMS is 31 degrees (from step 2). Therefore, angle JSM = 180 - 42 - 31 = 107 degrees.