Let A be the angle of 79 degrees
B be the angle of (5y-4) degrees
C be the angle of (x+5) degrees
D be the angle of (9z-7) degrees
According to the property of parallelogram
Opposite angles are equal
We get, angle A = angle C
Since angle A = 79 degrees
And angle C = (x+5) degrees
We get, x+5=79
=> x=79-5=74.

Angle B = Angle D
(5y-4)=(9z-7)
Since there’s two variables here, we can’t use the property of “opposite angles are equivalent”
We have to use another property which is adjacent angles are equal
Therefore, we can find angle D
Angle D + Angle A=180
=> 9z-7 =180-79
z=108/9
z=12
Since (5y-4)=(9z-7)
Substitute z=12 in
We get, 5y-4=101
y= 105/5
y= 21
Therefore, x=74, y=21 and z=12.

6 0

1 year ago

What is the lateral area of a regular square pyramid if the base edges are of length 24 and perpendicular height is 5?

iren2701 [21]

Answer:

The lateral area is 624 unit²

Step-by-step explanation:

* Lets explain how to solve the problem

- The regular square pyramid has a square base and four congruent

triangles

- The slant height of it = $\sqrt{(\frac{1}{2}b)^{2}+h^{2}}$ , where

b is the length of its base and h is the perpendicular height

- Its lateral area = $\frac{1}{2}.p.l$ , p is the perimeter of the base

and l is the slant height

* Lets solve the problem

∵ The base of the pyramid is a square with side length 24 units

∵ Its perpendicular height is 5 units

∵ The slant height (l) = $\sqrt{(\frac{1}{2}b)^{2}+h^{2}}$

∴ l = The slant height of it = $\sqrt{(\frac{1}{2}.24)^{2}+5^{2}}$

∴ l = $\sqrt{(12)^{2}+25}=\sqrt{144+25}=\sqrt{169}=13$

∴ l = 13 units

∵ Perimeter of the square = b × 4

∴ The perimeter of the base (p) = 24 × 4 = 96 units

∵ The lateral area = $\frac{1}{2}.p.l$

∴ The lateral area = $\frac{1}{2}.(96).(13)$

∴ The lateral area = 624 unit²

* The lateral area is 624 unit²

4 0

2 years ago

Lexi, susie and rial are playing an online word game. Rial scores 100,034 points. Lexi scores 9,348 fewer points than rial and s

Troyanec [42]

To solve this problem, you first need to subtract 100,034-9,348. You do this because Lexi scored that many points LOWER than Rial. You then take the answer to that subtraction problem (90,696) and add 9,749 to that answer. You do this because Susie scored 9,749 MORE than Lexi. You should get 100,435. This is Susie's score, so your final answer is 100,435 points.

3 0

2 years ago

What times 3 equals 3/10

Mumz [18]

Answer:

1/10

Step-by-step explanation:

Divide 3/10 by 3. Remember to "keep, flip, change".

3/10 ÷ 3/1

3/10 × 1/3

Multiply across: 3/10 × 1/3 = 3/30

Simplify: 3/30 = 1/10

7 0

2 years ago