Question

A regular pentagon ABCDE is fitted inside a regular hexagon APQRST such that P-B-Q, Q-C-R, R-D-S and S-E-T. Find m SED (in degrees).​

Answer 1

Step-by-step explanation:

3. Relate polynomial to daily life

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Answer 2

Answer:

When a regular pentagon is plotted inside a regular hexagon, the angle ∠ SED = 48°.

Step-by-step explanation:

Sum of interior angles in a regular polygon = (n-2) × 180.

Sum of interior angles in a triangle=180°.

Sum of angles in a linear pair =180°.

What is linear pair?

A linear pair is made when 2 lines intersected and 2 angles are formed, that is, when adjacent angles are formed. (Refer figure 1)

⇒ Sum of interior angles in a regular hexagon = 4 × 180 = 720 and sum of interior angles in a regular pentagon = 3 × 180 = 540.

Then, ∠ EAB = ∠ ABC =∠ BCD =∠ CDE =∠ AED = 108°. And ∠PAT=∠ATS=∠TSR =∠SRQ =∠RQP =∠APQ = 120°

Consider ∠ A, Where ∠EAB = 108°. Then, ∠PAB=∠TAE = $\frac{180-108}{2} = \frac{72}{2} =36$°.

Then using ∠TAE = 36° and ∠ATS=120°, consider triangle ΔATE , ∠AET= 180-(120+36) = 180-156 = 24°.

Hence, ∠SED = 180-(108+24)=48° (Refer figure 2).