All sides of a regular pentagon are extended to form a star with vertices P,Q,R,

Question

All sides of a regular pentagon are extended to form a star with vertices P,Q,R,S,T. What is the sum of the angles made at the vertices?___

Options:

Answer: Option A
:

Interior angle = [(2n-4)x90]/n = 108

2x= 360-(108x2) = 144

angle P = 180-144= 36

Total = 36x5= 180

Useful to remember: Sum of angles in a star= 180 $^{\circ}$

Shortcut: Clearly the star point trisects the angle in a pentagon. Hence each angle = 108/3 = 36.

Sum of angles = 36*5 = 180

Alternatively: Sum of angles of a n point star = (n – 4) x 180 $^{\circ}$ , where n = number of sides of a polygon.

Here, n = 5. Sum of angles of a n point star = (5 – 4) x 180 $^{\circ}$ = 180 $^{\circ}$ .

Was this answer helpful ?

Next Question

More Questions on This Topic :

Question 1. A square has two of its vertices on a circle and the other two are on the tangent to the circle. Find the area of the sq....if the radius of the circle is 5 units.

Question 2. Concentric circles are drawn with radii 1, 2, 3 … 100. The interior of the smallest circle is colored black and....regions divided by the area of the largest circle is

Question 3. What is the maximum number of times x circles of the same size can intersect each other? ....

Question 4. The interior angles of a polygon are in AP. If the smallest angle is 120∘ and the common difference is 5&#....then find the possible number of sides of that polygon?

Question 5. There is a circle of radius 10 units that circumscribes an equilateral triangle. A quadrilateral is drawn by joining m....sides of the triangle. Find the area of the quadrilateral

Question 6. If sin α= P and tan α= Q, find the value of 1P2−1Q2 ?....

Question 7. Find the side of a piece of cloth in the shape of an equilateral triangle, whose area costs as much to paint at Rs 10/....border around the three sides at Rs 25 per metre?

Question 8. In Δ ABC, D,E and F are taken on AB, AC and BC respectively, so that EF=CF and DF=BF. If ∠A=40∘, then find ∠DFE....respectively, so that EF=CF and DF=BF. If ∠A=40∘, then find ∠DFE?

Question 9. If O is the centre of a circle and the radius of the circle is 4 units, find the value of length of AC.....

Question 10. What is the circumradius of a triangle whose sides are 7, 24 and 25 respectively? ....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

DSP Combined 1 Free Revision Test SAIL JO E-0

GPOE / GPA Combined 1 Free Revision Test SAIL JO E-0

BSP Plant Specific Review Test SAIL JO E-0

BSL Combined 1 Free Revision Test SAIL JO E-0

GFM Combined 1 Free Revision Test SAIL JO E-0