Given:
In an isosceles triangle LMN, LM=MN.
[tex]m\angle M=(3x+17)^\circ,m\angle L=(2x+36)^\circ[/tex]
To find:
The measure of the angles L, M and N.
Solution:
In triangle LMN,
[tex]LM=MN[/tex] (Given)
[tex]m\angle N=m\angle L=(2x+36)^\circ[/tex] (Base angles of an isosceles triangle are equal)
Now,
[tex]m\angle L+m\angle M+m\angle N=180^\circ[/tex]
[tex](2x+36)^\circ+(3x+17)^\circ+(2x+36)^\circ=180^\circ[/tex]
[tex](7x+89)^\circ=180^\circ[/tex]
[tex](7x+89)=180[/tex]
On further simplification, we get
[tex]7x=180-89[/tex]
[tex]7x=91[/tex]
[tex]x=\dfrac{91}{7}[/tex]
[tex]x=13[/tex]
The value of x is 13. Using this value, we get
[tex]m\angle L=(2(13)+36)^\circ[/tex]
[tex]m\angle L=(26+36)^\circ[/tex]
[tex]m\angle L=62^\circ[/tex]
Similarly,
[tex]m\angle M=(3(13)+17)^\circ[/tex]
[tex]m\angle M=(39+17)^\circ[/tex]
[tex]m\angle M=56^\circ[/tex]
And,
[tex]m\angle N=m\angle L[/tex]
[tex]m\angle N=62^\circ[/tex]
Therefore, the measure of angles are [tex]m\angle L=62^\circ,m\angle M=56^\circ,m\angle N=62^\circ[/tex].
