4. the measure of the exterior angle of an octagon are m°,2m°,3m°,4m°,5m°,6m°,7m...

Questions

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October 2022 1 4 Report

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.?

Answers & Comments

Axlr8

SOLUTION:

Recall:

The sum of all exterior angles of any convex polygon is equal to $360^{\circ}.$

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

For number 4:

$\small m^{\circ} + 2m^{\circ} + 3m^{\circ} + 4m^{\circ} + 5m^{\circ} + 6m^{\circ} + 7m^{\circ} + 8m^{\circ} = 360^{\circ}$

Solving for $m,$

$36m^{\circ} = 360^{\circ}$

$m = \dfrac{360}{36}$

$\boxed{m = 10}$

For number 5:

Let $2x$ and $3x$ be the measures of the other two angles of the pentagon.

$105^{\circ} + 135^{\circ} + 120^{\circ} + 2x + 3x = (5 - 2)(180^{\circ})$

$360^{\circ} + 5x = 540^{\circ}$

$5x = 540^{\circ} - 360^{\circ}$

$5x = 180^{\circ}$

$x = \dfrac{180^{\circ}}{5}$

$x = 36^{\circ}$

Substituting the value of x, we get

$2x = 2(36^{\circ}) = \boxed{72^{\circ}}$

$3x = 3(36^{\circ}) = \boxed{108^{\circ}}$

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

abegailabin5gmailcom salamat pero yung sagot sa 4 is 10

Axlr8 Ay, wait, na misread ko

Axlr8 Ieedit ko lang

vPatriciax can someone answer me this

vPatriciax Three angles of a pentagon are 115, 125 and 135. Find the other two angels in the ratio of 2:3

bunnelby pede paexplain kung san nakuha yung 540 sa #5

mrbinibini wala po sa pagpipilian yung 5

markraysampang Three angles of a pentagon are 115, 125 and 135. Find the other two angels in the ratio of 2:3?

Answer:
72° and 128°

markraysampang Solution:
Three angles of a pentagon are 105°, 135°, and 120°.

Let N represents the other 2 angles of the pentagon.

540° - (105° + 135° + 120°) = N

540° - 360° = N

180° = N

If the other two angles of the pentagon has a sum of 180°, find the measure of each using the ratio 2:3.

Let x be the angle measure.

2x + 3x = 180

5x = 180

=

x = 36°

Using x = 2 find the angle measures.

2x = 2(36) = 72°

3x = 3(36) = 108°

Therefore, the measures of the other two angles of the pentagon are 72° and 108° respectively.