Question

$▱\mathrm{DECK}$is a parallelogram. Complete.

If $\mathrm{m}\angle 1=42,\mathrm{m}\angle 2={\mathrm{x}}^2$and $\mathrm{m}\angle \mathrm{CED}=13\mathrm{x}$then $\mathrm{m}\angle 2=?$or $\mathrm{m}\angle 2=?$(numerical answers).

Short answer

The value of $m\angle 2$is $36°$or $49°$.

Step-by-step solution

Step 1. Apply property of parallelogram.

The opposite angles of a parallelogram are congruent.

From the given figure, it can be observed that $\angle K$and $\angle E$are opposite angles, such that,

$\begin{array}{c}m\angle 1+m\angle 2=m\angle CED\\ 42+x^2=13x\\ x^2-13x+42=0\end{array}$

Step 2. Solve the quadratic equation.

Solve the obtained quadratic equation in step 1 to find the value of x.

$\begin{array}{l}{x}^2-13x+42=0\\ x^2-6x-7x+42=0\\ x\left(x-6\right)-7\left(x-6\right)=0\\ x-6=0\text{or}x-7=0\\ x=6\text{orx}=7\end{array}$

Solving equation $x^2-3x-70=0$gives the roots as, $x=6\text{or}x=7$.

Step 3. Description of step.

Substitute 6 for x into $m\angle 2=x^2$to find the value of $m\angle 2$.

$\begin{array}{c}m\angle 2=x^2\\ =6^2\\ =36°\end{array}$

Step 4. Description of step.

Substitute 7 for x into $m\angle 2=x^2$to find the value of $m\angle 2$.

$\begin{array}{c}m\angle 2=x^2\\ =7^2\\ =49°\end{array}$

Therefore, the value of $m\angle 2$is $36°$or $49°$.