question_answer

Draw any rectangle and find the measures of angles at the four vertices made by the intersecting lines.

Answer:

Let ABCD be the rectangle. ABCD is a parallelogram with \[\angle A=90{}^\circ \] We have, \[\angle C=\angle A=90{}^\circ \] (opposite angles of a parallelogram are equal) Again, \[\angle A+\angle B=180{}^\circ \] \[(\because \angle A\text{ }and\angle B\text{ }are\text{ }adjacent\text{ }angles\text{ }of\text{ }\] \[a\text{ }parallelogram)\] \[90{}^\circ +\angle B=180{}^\circ \] \[\angle B=180{}^\circ 90{}^\circ =90{}^\circ \] ∴ \[\angle D=\angle B=90{}^\circ \] (\[\because \]opposite angles of a parallelogram are equal) Hence, \[\angle A=\angle B=\angle C=\angle D=90{}^\circ \].