Question

Algebra Find the value(s) of the variables in each kite.

Answer 1

56º,34º

1) A kite is a quadrilateral that according to the following theorem:

2) And examining that picture, we can tell that the angle labeled as 8x is congruent to its opposite counterpart.

3) In addition to this, but not less important that bigger diagonal bisects that the other pair of opposite angles. So we can sketch the following

So we can pick one triangle and write out the following according to the Triangle sum theorem:

`\begin{gathered} 8x+(5x-1)+90=180 \\ 8x+5x-1+90=180 \\ 13x+89=180 \\ 13x=180-89 \\ (13x)/(13)=(91)/(13) \\ x=7 \end{gathered}`

4) Finally, let's plug into each one the quantity of x and get the measure of those angles: