Question

Find x, if the angles of a triangle have measures $(x+{40}^0),(2x+{20}^0)and3x$

also state which type of triangle is this.

• A. $x={60}^{\circ }$ and Equilateral triangle
• B. $x={20}^{\circ }$ and Scalene triangle
• C. $x={20}^{\circ }$ and Equilateral triangle
• D. $x={40}^{\circ }$ and Scalene triangle

Answer 1

The correct option is C $x={20}^{\circ }$ and Equilateral triangle

The angles of the triangle are $(x+{40}^o),(2x+{20}^o),3x$. Thus,

$x+{40}^o+2x+{20}^o+3x={180}^o$

$6x+{60}^o={180}^o$

$6x={120}^o$

$x={20}^o$

Thus, the angles are ${60}^o,{60}^o,{60}^o$. Hence, the triangle is an equilateral triangle.