Question

the figures show a square a regular Pentagon and a regular hexagon put together find the angles
< DAE
< DAB
< CAE
< BAC
​

Answer 1

Step-by-step explanation:

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

⇒ Sum of all interior angle divided by number of side

= 540°/5 = 108°

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

⇒ Sum of all interior angle divided by number of side

= 720°/6 =120

Let us assume the point opposite

∠ PQS + ∠ RQS + ∠ PQR = 360° (pair of angles at a vertex)

⇒ 120° + 108° + ∠ PQR = 360°

⇒ 228° + ∠ PQR = 360°

⇒ ∠ PQR = 360° - 228°

⇒ ∠ PQR = 132°

I HOPE THIS IS HELPFUL.