91Ó°ÊÓ

Opposite angles of a parallelogram are congruent, that is they are equal on measure.

In a given figure, by the property of a parallelogram,

$\begin{array}{c}m∠B=m∠D\\ =80°\end{array}$

$\begin{array}{c}m∠A=m∠C\\ 5x+6y+5=35+m∠ACB\end{array}$

The sum of measures of all the angles of a triangle is 180.

Consider $\mathrm{Δ}ADC$, such that,

$\begin{array}{c}m∠ADC+m∠DCA+m∠DAC=180\\ 80+35+5x=180\\ 115+5x=180\\ 5x=65\end{array}$

Divide each side of $5x=65$ by 5 to obtain the value of x.

$\begin{array}{c}\frac{5x}{5}=\frac{65}{5}\\ x=13\end{array}$

The sum of measures of all the angles of a triangle is 180.

Consider $\mathrm{Δ}ABC$, such that,

$\begin{array}{c}m∠ACB+m∠ABC+m∠BAC=180\\ m∠ACB+80+6y+5=180\\ m∠ACB+6y=95\\ m∠ACB=95−6y\end{array}$

Substitute $95−6y$for $m∠ACB$and 13 for into $5x+6y+5=35+m∠ACB$ to find the value of y.

$\begin{array}{c}5x+6y+5=35+95−6y\\ 5×13+6y+5=35+95−6y\\ 12y=60\\ y=5\end{array}$

Therefore, the value of x and y is 13 and 5 respectively.