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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$m\angle C:m\angle D=1:5$.