Answer:
B.[tex]22^{\circ}[/tex]
Step-by-step explanation:
We are given that HMS is an isosceles triangle.
Angle M is the vertex angle.
[tex]m\angle M=(2x+6)^{\circ}[/tex]
[tex]m\angle H=(9x+7)^{\circ}[/tex]
[tex]\angle H=\angle S[/tex]
By definition of isosceles triangle
We have to find the measure of angle M.
[tex]\angle M+\angle H+\angle S=180^{\circ}[/tex]
By using sum of angles of triangle property
Substitute the values
[tex]2x+6+9x+7+9x+7=180[/tex]
[tex]20x+20=180[/tex]
[tex]20x=180-20[/tex]
[tex]20x=160[/tex]
[tex]x=\frac{160}{20}=8[/tex]
Using the value of x
[tex]m\angle M=2(8)+6[/tex]
[tex]m\angle M=22^{\circ}[/tex]
Hence, option B is correct.
