In a triangle RSM, the measure of angle SRM is twice the measure of angle RSM. A point O is selected on side RS such that SO=SM. The length of the angle bisector of angle RMS equals RO. What is the degree measure of angle RSM. The answer is a positive integer.

Question

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Respuesta :

nuuk nuuk · Answer 1 · 2020-05-13T13:04:03+02:00

Answer:[tex]36^{\circ}[/tex]

Step-by-step explanation:

Given

[tex]\angle RSM =2\angle SRM[/tex]

suppose [tex]\angle RSM =\angle 2[/tex]

and [tex]\angle SRM=1[/tex]

So from figure

[tex]\angle SOM =\angle OMS=\angle 3[/tex]

and [tex]\angle OMS=\angle 0MR[/tex]

In triangle [tex]SOM[/tex]

[tex]\angle 2+\angle 3+\angle 3=180^{\circ}[/tex]

[tex] \angle 2+2\angle 3=180^{\circ}\quad \ldots(i)[/tex]

In triangle [tex]RSM[/tex]

[tex]\angle 1+\angle 2+\angle 3=180^{\circ}\quad \ldots(ii)[/tex]

and [tex]\angle 1=2\angle 2[/tex]

Using this and Substitute this value in [tex](ii)[/tex]

[tex]2\angle 2+\angle 2+\angle 3=180^{\circ}[/tex]

[tex]3\angle 2+\angle 3=180^{\circ}\quad \ldots(iii)[/tex]

Solving (i) and (iii) we get

[tex]2\angle 2=\angle 3[/tex]

Substitute in equation (i) we get

So [tex]\angle 2=\frac{180}{5} [/tex]

[tex]\angle 2=36^{\circ}[/tex]

So [tex]\angle RSM=\angle 2=36^{\circ}[/tex]