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Expert-verified Found in: Page 212 ### Geometry

Book edition Student Edition
Author(s) Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen
Pages 227 pages
ISBN 9780395977279 # Prove the following statement by proving its contrapositive. Begin by writing what is given and what is to be proved. If $m\angle A+m\angle B\ne 180°$ then $m\angle D+m\angle C\ne 180°$. Hence proved that if $m\angle A+m\angle B\ne 180°$ then $m\angle D+m\angle C\ne 180°$.

See the step by step solution

## Step 1. Define contrapositive statement

If the given statement is ‘’If p then q’’, the contrapositive is ‘’If not q then not p’’.

The given statement is if $m\angle A+m\angle B\ne 180°$ then $m\angle D+m\angle C\ne 180°$.

## Step 2. Let the given statement and find its contrapositive

The contrapositive of the given statement is if $m\angle D+m\angle C=180°$ then $m\angle A+m\angle B=180°$.

## Step 3. Prove the statement

Since the sum of all angles of a quadrilateral is 360, therefore following will hold from the given figure as:

$\begin{array}{c}m\angle A+m\angle B+m\angle D+m\angle C=360°\\ m\angle A+m\angle B+{180}^{o}=360°\\ m\angle A+m\angle B=360°-180°\\ m\angle A+m\angle B=180°\end{array}$ ### Want to see more solutions like these? 