Answered

At Westonci.ca, we make it easy for you to get the answers you need from a community of knowledgeable individuals. Experience the convenience of getting accurate answers to your questions from a dedicated community of professionals. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

In a pentagon, the second angle is twice the first but half of the fourth, third angle is three times the first and the fifth angle is 20° less than the fourth. Find all the angles.​

Sagot :

sreedevi102

Answer:

[tex]First\ angle = x = 40^\circ\\\\Second\ angle = 2x = 2 \times 40 = 80^\circ\\\\Third \ angle = 3x = 3 \times 40 = 120^\circ\\\\Fourth \ angle = 4x = 4\times 40 = 160^\circ\\\\Fifth\ angle = (4x - 20) = ( 4 \times 40) - 20 = 160 -20 = 140^\circ[/tex]

Step-by-step explanation:

Let the first angle be  = x

Given:

           Second angle is twice first = 2x

           Third angle is three times first = 3x

Also given:

  Second angle is half of fourth angle, that is:

                                                                   [tex]2x = \frac{1}{2} \times 4 ^{th} angle\\\\4^{th} angle = 2x \times 2 = 4x[/tex]

 Fifth angle is 20° less than fourth angle, that is:

                                                                   [tex]4x - 20^\circ[/tex]

Sum of interior angles of a polygon with n sides = ( n - 2 ) x 180°

Here n = 5 ,

   therefore sum of interior angles = ( 5 - 2 ) x 180 = 3 x 180 = 540°.

That is ,

             x + 2x + 3x + 4x + ( 4x - 20 )  = 540

                                           14x - 20 = 540

                                                  14x = 540 + 20

                                                  14x = 560

                                                     x = 40

[tex]Therefore, \\\\First\ angle = x = 40^\circ\\\\Second\ angle = 2x = 2 \times 40 = 80^\circ\\\\Third \ angle = 3x = 3 \times 40 = 120^\circ\\\\Fourth \ angle = 4x = 4\times 40 = 160^\circ\\\\Fifth\ angle = (4x - 20) = ( 4 \times 40) - 20 = 160 -20 = 140^\circ[/tex]

Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.