Question

The given figure shows a square, an equilateral triangle and a regular hexagon put together. Which of the following statements is true?

• A. $\angle ABC={100}^{\circ }$
• B. $\angle ABC={90}^{\circ }$
• C. $AB=BC$
• D. $\angle BAC={45}^{\circ }$

Answer 1

Answer: (B), (C), (D)

The correct options are
B

$\angle ABC={90}^{\circ }$

C

$AB=BC$

D

$\angle BAC={45}^{\circ }$

(i) Each interior angle of an equilateral triangle is = ${60}^{\circ }$

Each interior angle of a regular hexagon is = ${120}^{\circ }$

Each interior angle of a square is = ${90}^{\circ }$

$\angle ABC={360}^{\circ }-({90}^{\circ }+{60}^{\circ }+{120}^{\circ })$

$={360}^{\circ }-{270}^{\circ }$

$={90}^{\circ }$

(ii) AB = BC (side of square = side of hexagon)

(iii) $\angle BAC=\angle BCA=\frac{{180}^{\circ }-{90}^{\circ }}{2}$

$={45}^{\circ }$