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:
210 yd³
Step-by-step explanation:
V=LWH
V=(8 1/3)(4 1/5)(6)
V=(25/3)(21/5)(6)
V=(525/15)(6)
V=3150/15
V=210
Therefore, the volume of the prism is 210 yd³
Multiplication is the process of multiplying. The amount of medicine that Lamar's dog will have in one week is 25.2 milligrams.
<h3>What is multiplication?</h3>
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given a medicine provides 3.6 milligrams of medicine. Therefore, the amount of medicine the dog will have in a week is,
The amount of medicine = 3.6milligrams × 7 = 25.2 milligrams
Hence, the amount of medicine that Lamar's dog will have in one week is 25.2 milligrams.
Learn more about Multiplication:
brainly.com/question/14059007
#SPJ1
Answer:
C and E repr. constant functions.
Step-by-step explanation:
C and E represent constant functions. One can tell immediately by the fact that y remains the same even when x changes.
Answer:
<u>The smallest angle measures 13°, the largest angle measures 91° and the third angle measures 76°</u>
Step-by-step explanation:
Let's recall that the interior angles of a triangle add up to 180°, therefore we have:
Smallest angle = x
Largest angle = 7x
Third angle = 7x - 15
Now, we can solve for x, using the following equation:
x + 7x + 7x - 15 = 180
15x = 180 + 15
15x = 195
x = 195/15
x = 13 ⇒ 7x = 91 ⇒ 7x - 15 = 76
<u>The smallest angle measures 13°, the largest angle measures 91° and the third angle measures 76°</u>
