Answer: Angle x equals 19 degrees
Step-by-step explanation: We have two polygons, one with five sides and the other with eight sides. The question states that the pentagon has exactly one line of symmetry which means the line that runs down from point D to line AB divides the shape into exactly two equal sides. Hence angle A measures the same size as angle B (in the pentagon).
First step is to calculate the angles in the pentagon. The sum of angles in a polygon is given as
(n - 2) x 180 {where n is the number of sides}
= 3 x 180
= 540
This means the total angles in the pentagon can be expressed as
A + B + 84 + 112 + 112 = 540
A + B + 308 = 540
Subtract 308 from both sides of the equation
A + B = 232
Since we have earlier determined that angle A measures the same size as angle B, we simply divide 232 into two equal sides, so 232/2 = 116
Having determined angle A as 116 degrees, we can now compute the value of angle A in the octagon ABFGHIJK. Since the figure is a regular octagon, that means all the angles are of equal measurement. So, the sum of interior angles is given as
(n - 2) x 180 {where n is the number of sides}
= 6 x 180
= 1080
If the total sum of the interior angles equals 1080, then each angle becomes
1080/8
= 135 degrees.
That means angle A in the octagon measures 135, while in the pentagon it measures 116. The size of angle x is simply the difference between both values which is
x = 135 - 116
x = 19 degrees
Answer:
40kg
20kg
10kg
Step-by-step explanation:
The computation of the food each one is getting as follows
Total weights of all dogs
= 20 kg + 10 kg + 5kg
= 35 kg
And, the food is 70 kg
So, each one is getting
for 20 kg
= 70 ÷ 35 × 20
= 40 kg
For 10 kg
= 70 ÷ 35 × 10
= 20 kg
And, for 5 kg
= 70 ÷ 35 × 5
= 10 kg
35,894 rounded to the greatest place is 36,000
Answer:x
Step-by-step explanation:
