6Hello there. To solve this question, we'll have to remember some properties about parallelograms.
Given the parallelogram RODY, and the measure of the angles as functions of a variable x:
[tex]\begin{gathered} m\angle R=(7x+22)^{\circ} \\ m\angle O=(9x-2)^{\circ} \end{gathered}[/tex]We have to determine the measure of the angle R.
For this, we'll have to remember the following property about parallelograms:
The sides with one and two lines have the same measure, respectively.
Now imagine the following angles:
And that we move this triangle to the other side, that is:
With this, you notice that the angles might be supplementary, or mathematically it is the same as:
[tex]\alpha+\beta=180^{\circ}[/tex]We also know that the angle at R might be:
When we moved the triangle, we now have that:
[tex]m\angle R-(90^{\circ}-\alpha)=m\angle R-90^{\circ}+\alpha=90^{\circ}\Rightarrow m\angle R=180^{\circ}-\alpha=\beta[/tex]So the measure of the angle at O will be:
[tex]m\angle O=\alpha[/tex]In the end, we reached the equation we need to solve:
[tex]m\angle R+m\angle O=180^{\circ}[/tex]Plugging the measures in function of x, we get
[tex](7x+22)^{\circ}+(9x-2)^{\circ}=180^{\circ}[/tex]Add the values
[tex]16x+20^{\circ}=180^{\circ}[/tex]Subtract 20º on both sides of the equation
[tex]16x=160^{\circ}[/tex]Divide both sides of the equation by a factor of 16
[tex]x=10^{\circ}[/tex]Now, to find the measure of the angle R, simply plug the value of x:
[tex]m\angle R=(7\cdot10+22)^{\circ}=(70+22)^{\circ}=92^{\circ}[/tex]This is the answer we were looking for.
is:
With this, you notice that the angles might be supplementary, or mathematically it is the same as:
