Abegailabin5gmailcomidn
Answered

IDNStudy.com, kung saan ang kuryusidad ay nagtatagpo ng kalinawan. Makakuha ng mabilis at eksaktong sagot sa iyong mga tanong mula sa aming mga eksperto na laging handang tumulong.

4. the measure of the exterior angle of an octagon are m°,2m°,3m°,4m°,5m°,6m°,7m°, and 8m° what is the value of m?
5.three angles of a pentagon are 105°,135° and 120° ,find the other two angles if they are in the ratio 2:3.?​

Sagot :

Axlr8idn

SOLUTION:

Recall:

  • The sum of all exterior angles of any convex polygon is equal to [tex]360^{\circ}.[/tex]

  • The sum of all interior angles of a convex n-sided polygon is given by the formula: [tex] (n - 2)180^{\circ} [/tex]

For number 4:

[tex] \small m^{\circ} + 2m^{\circ} + 3m^{\circ} + 4m^{\circ} + 5m^{\circ} + 6m^{\circ} + 7m^{\circ} + 8m^{\circ} = 360^{\circ} [/tex]

Solving for [tex] m,[/tex]

[tex] 36m^{\circ} = 360^{\circ} [/tex]

[tex] m = \dfrac{360}{36} [/tex]

[tex]\boxed{m = 10} [/tex]

For number 5:

Let [tex]2x[/tex] and [tex] 3x[/tex] be the measures of the other two angles of the pentagon.

[tex] 105^{\circ} + 135^{\circ} + 120^{\circ} + 2x + 3x = (5 - 2)(180^{\circ}) [/tex]

[tex] 360^{\circ} + 5x = 540^{\circ} [/tex]

[tex] 5x = 540^{\circ} - 360^{\circ} [/tex]

[tex] 5x = 180^{\circ} [/tex]

[tex] x = \dfrac{180^{\circ}}{5} [/tex]

[tex] x = 36^{\circ} [/tex]

Substituting the value of x, we get

[tex] 2x = 2(36^{\circ}) = \boxed{72^{\circ}} [/tex]

[tex] 3x = 3(36^{\circ}) = \boxed{108^{\circ}} [/tex]

Thus, the other two angles measure 72° and 108°.