Question

Manu has decided to create a triangular flower bed border. He plans to use 3 pieces of rectangular wooden plates with lengths $4,5$ and $6$ feet, as shown in the figure.
Manu plans to cut the 3 pieces of plate for the flower bed border from a single piece of plate. The measure of $\angle ABC$ in the figure is $x^o$. Which of the following is an expression for ${\beta }^o$?

• A. $x^o$
• B. $2x^o$
• C. ${(90+x)}^o$
• D. ${(180-x)}^o$
• E. ${(180-\frac{x}{2})}^o$

Answer 1

Answer: (D)

${(180-x)}^o$

The angle of the edges of the wood is ${90}^0$ and the sum total of the angles $x^0$ ${\beta }^0$ and two edges of the wood is ${360}^0$. Hence $x^0+{\beta }^0+2\left({90}^0\right)={360}^0$

$\Rightarrow x^0+{\beta }^0+{180}^0={360}^0$

$\Rightarrow x^0+{\beta }^0={180}^0$

$\Rightarrow {\beta }^0={180}^0-x^0$