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Q3.

Expert-verified
Found in: Page 243

Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279

ABCD is a parallelogram. Find the value of each ratio.$m\angle C:m\angle D$

The simplest form of $m\angle C:m\angle D=1:5$

See the step by step solution

Step 1. Given information.

According to the given figure is,

In parallelogram,

$\begin{array}{l}m\angle C={30}^{\circ }\\ m\angle D={150}^{\circ }\end{array}$

Write the ratio,

$\begin{array}{l}m\angle C:m\angle D=30:150\\ \frac{m\angle C}{m\angle D}=\frac{30}{150}\end{array}$

Step 2. Concept Used.

To write the fraction in simplest form, divide the numerator and denominator with the GCF (Greatest Common Factor).

Step 3. Now find the GCF.

Write the prime factors of numerator and denominator.

$\begin{array}{l}30=2×3×5\\ 150=2×3×5×5\end{array}$

Here GCF is.$2×3×5=30$

Step 4. Let’s divide the numerator and denominator with the GCF.

Here we will divide the numerator and denominator by30 v.

$\frac{30}{150}=\frac{30/30}{150/30}=\frac{1}{5}$

Therefore, the simplest form of the given ratio is$m\angle C:m\angle D=1:5$.