Q. 74.7( 7 Votes )

# The figure shows a square, a regular pentagon and a regular hexagon put together. How much is ∠BAC?

Answer :

We know that, all angles of square are 90°.

In regular pentagon,

Sum of the angles of n-sided polygon = (n – 2) × 180°

⇒ S = (5 – 2) × 180°

⇒ S = 3 × 180°

⇒ S = 540°

Measure of each interior angle

⇒

In regular hexagon,

Sum of the angles of n-sided polygon = (n – 2) × 180°

⇒ S = (6 – 2) × 180°

⇒ S = 4 × 180°

⇒ S = 720°

Measure of each interior angle

⇒

Let us assume the two points adajacent A as P and L.

∠ BAP + ∠ BAC + ∠ CAL + ∠ PAL = 360° (pair of angles at a vertex)

⇒ 120° + 108° + 90° + ∠ BAC = 360°

⇒ 318° + ∠ BAC = 360°

⇒ ∠ BAC = 360° - 318°

⇒ ∠ BAC = 42°

Rate this question :

One angle of a regular polygon is 168°. How many sides does it have?

Kerala Board Mathematics Part IIn the figure, ABCDEF is a regular hexagon. Prove that ACDF is a rectangle.

Kerala Board Mathematics Part I

The figure shown a regular pentagon and a regular hexagon put together. How much is ∠PQR?

Kerala Board Mathematics Part I

Draw a hexagon of equal angles and unequal sides.

Kerala Board Mathematics Part IIn the figure, ABCDEF is a regular hexagon. Prove that ΔBDF, drawn joining alternate vertices is equilateral.

Kerala Board Mathematics Part I

The figure shows a square, a regular pentagon and a regular hexagon put together. How much is ∠BAC?

Kerala Board Mathematics Part I

How much is each angle of a 15-sided regular polygon? How much is each outer angle?

Kerala Board Mathematics Part IIn a regular polygon, the ratio of the ratio of the inner and outer angle is 7 : 2. What is each angle? How many sides does the polygon have?

Kerala Board Mathematics Part IICan we draw a regular polygon with each outer angle 6°? What about 7°?

Kerala Board Mathematics Part IDraw a hexagon of equal sides and unequal angles.

Kerala Board Mathematics Part I