Question

the measure of two consecutive angles in a parallelogram are in a 13:7 ratio. What is the measure of the acute angle in the parallelogram

Answer 1

In a parallelogram, consecutive angles are supplementary angles.

Let a and b be two consecutive angles in a parallelogram, so that their ratio is 13:7. Then:

$\frac{a}{b}=\frac{13}{7}$

Since they are supplementary angles, then:

$a+b=180$

Isolate a from the first equation and substitute the expression for a in the second equation:

$\begin{gathered} a=\frac{13}{7}b \\ \frac{13}{7}b+b=180 \\ \Rightarrow\frac{20}{7}b=180 \\ \Rightarrow b=\frac{7}{20}\times180 \\ \Rightarrow b=63 \end{gathered}$

The value of a can be calculated from any of the equations from the value of b, and turns out to be equal to 117.

From the angles 117° and 63°, the acute angle is 63°.

Therefore, the measure of the acute angle in the parallelogram, is:

$63^{\circ}$