Question

The given figure shows a square and a regular pentagon put together. Which of the following statements is true?

• A. $\angle ABC={162}^{\circ }$
• B. $\angle BAC=\angle BCA={18}^{\circ }$
• C. $\angle BAC=\angle BCA=9^{\circ }$
• D. BA=BC

Answer 1

Answer: (A), (C), (D)

The correct options are
A

$\angle ABC={162}^{\circ }$

C

$\angle BAC=\angle BCA=9^{\circ }$

D

BA=BC

(i) AB=BC

(side of square = side of pentagon)

(ii) Each angle of a square is ${90}^{\circ }$

Each angle of a pentagon is ${108}^{\circ }$

$\therefore \angle ABC={360}^{\circ }-({108}^{\circ }+{90}^{\circ })$

$\angle ABC={360}^{\circ }-{198}^{\circ }$

$\angle ABC={162}^{\circ }$

(iii) $\angle BAC=\angle BCA=\frac{{180}^{\circ }-{162}^{\circ }}{2}$

$=9^{\circ }$