Question

The angles of a triangle are $2(x-7)$ , $\frac{3}{2}(x-1)$ and $3(x+11)$ . Find $x$ and then show that the triangle is isosceles.

• A. $15$
• B. $18$
• C. $22$
• D. $25$

Answer 1

The correct option is D $25$

Sum of the angles $=180$

$2(x-7)+\frac{3}{2}(x-1)+3(x+11)=180LCM=24(x-7)+3(x-1)+6(x+11)=3604x-28+3x-3+6x+66=36013x+35=36013x=325x=25$

Angle $1=2(x-7)=2\left(18\right)=36$

Angle $2=\frac{3}{2}(x-1)=\frac{3}{2}\left(24\right)=36$

Since two angles are equal, it is an isosceles triangle.