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Q21.

Expert-verifiedFound in: Page 212

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 $m\angle A+m\angle B\ne 180\xb0$ then $m\angle D+m\angle C\ne 180\xb0$.

Hence proved that if $m\angle A+m\angle B\ne 180\xb0$ then $m\angle D+m\angle C\ne 180\xb0$.

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

The given statement is if $m\angle A+m\angle B\ne 180\xb0$ then $m\angle D+m\angle C\ne 180\xb0$.

The contrapositive of the given statement is if $m\angle D+m\angle C=180\xb0$ then $m\angle A+m\angle B=180\xb0$.

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

$\begin{array}{c}m\angle A+m\angle B+m\angle D+m\angle C=360\xb0\\ m\angle A+m\angle B+{180}^{o}=360\xb0\\ m\angle A+m\angle B=360\xb0-180\xb0\\ m\angle A+m\angle B=180\xb0\end{array}$

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