Question

In the diagram AJEA below, mZJEA=90 and mZEAJ = 48. Line segment MS connectspoints M and S on the triangle, such that m ZEMS = 59.What is mZMSA?1) 1632) 1213) 424) 17

Answer 1

Given data;

The ∠JAE =48 degrees.

The measure of the ∠EAJ =90 dgrees.

The measure of the ∠MES=59 degree.

In triangle JEA

∠JAE+∠EAJ+∠EJA=180 degree

Substitute the given values in the above expression.

48 degree+90 degree+∠EJA=180 degree

∠EJA=42 degree.

The angle JMS is,

∠JMS=180-∠MES

∠JMS=180 degree-59 degree

=121 degree.

In triangle JMS,

∠JMS+∠JSM+∠EJA=180 degree

121 degree+∠JSM+42 degree=180 degree

∠JSM=17 degree

The angle MSA is,

∠MSA=180 degree-∠JSM

=180 degree-17 degree

=163 degree

Thus, the ∠MSA is 163 degree first option is correct.