Photo AI

A student draws two different regular polygons - OCR - GCSE Maths - Question 25 - 2023 - Paper 2

Question icon

Question 25

A-student-draws-two-different-regular-polygons-OCR-GCSE Maths-Question 25-2023-Paper 2.png

A student draws two different regular polygons. The exterior angle of one polygon is $p^{\circ}$. The exterior angle of the other polygon is $q^{\circ}$. The sum of... show full transcript

Worked Solution & Example Answer:A student draws two different regular polygons - OCR - GCSE Maths - Question 25 - 2023 - Paper 2

Step 1

The sum of p and q is 112°

96%

114 rated

Answer

We start with the equations derived from the statement:

  1. p+q=112p + q = 112 (Equation 1)
  2. p−q=32p - q = 32 (Equation 2)

To solve for pp and qq, we can add both equations:

(p+q)+(p−q)=112+32(p + q) + (p - q) = 112 + 32

This simplifies to:

2p=1442p = 144

Thus,

p=72∘p = 72^{\circ}

Step 2

The difference between p and q is 32°

99%

104 rated

Answer

Next, we substitute p=72∘p = 72^{\circ} back into Equation 1:

72+q=11272 + q = 112

Thus,

q=112−72=40∘q = 112 - 72 = 40^{\circ}

Step 3

Find the number of sides of each polygon

96%

101 rated

Answer

The exterior angle of a regular polygon is given by the formula:

Exterior Angle=360∘n\text{Exterior Angle} = \frac{360^{\circ}}{n}

Where nn is the number of sides of the polygon.

For the first polygon (with exterior angle p=72∘p = 72^{\circ}):

72=360n1 ⇒n1=36072=572 = \frac{360}{n_1} \ \Rightarrow n_1 = \frac{360}{72} = 5

For the second polygon (with exterior angle q=40∘q = 40^{\circ}):

40=360n2 ⇒n2=36040=940 = \frac{360}{n_2} \ \Rightarrow n_2 = \frac{360}{40} = 9

Thus, the number of sides of each polygon is:

5 sides and 9 sides.

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;