Answer:
x = 8
measure of each side = 27 units
Step-by-step explanation:
Properties of an <u>equilateral triangle</u>:
- Regular polygon with 3 sides
- All 3 sides are <u>equal in length</u>
- All 3 interior angles are congruent
If ΔGHJ is an equilateral triangle, the side measures are equal.
![\implies \sf GH = HJ = GJ](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20GH%20%3D%20HJ%20%3D%20GJ)
![\implies (5x-13)=(11x-61)=(7x-29)](https://tex.z-dn.net/?f=%5Cimplies%20%285x-13%29%3D%2811x-61%29%3D%287x-29%29)
To solve for x, choose 2 side lengths, equate them, and solve for x:
![\implies \sf GH=HJ](https://tex.z-dn.net/?f=%5Cimplies%20%5Csf%20GH%3DHJ)
![\implies 5x-13=11x-61](https://tex.z-dn.net/?f=%5Cimplies%205x-13%3D11x-61)
![\implies 5x-13 - 5x =11x-61 - 5x](https://tex.z-dn.net/?f=%5Cimplies%205x-13%20-%205x%20%3D11x-61%20-%205x)
![\implies -13=6x-61](https://tex.z-dn.net/?f=%5Cimplies%20-13%3D6x-61)
![\implies -13+61=6x-61+61](https://tex.z-dn.net/?f=%5Cimplies%20-13%2B61%3D6x-61%2B61)
![\implies 48=6x](https://tex.z-dn.net/?f=%5Cimplies%2048%3D6x)
![\implies 48 \div 6=6x \div 6](https://tex.z-dn.net/?f=%5Cimplies%2048%20%5Cdiv%206%3D6x%20%5Cdiv%206)
![\implies x=8](https://tex.z-dn.net/?f=%5Cimplies%20x%3D8)
To find the measure of each side, substitute the found value of x into one of the side expressions:
![\begin{aligned}\implies \textsf{GH}&=5(8)-13\\& =40-13\\& =27\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cimplies%20%5Ctextsf%7BGH%7D%26%3D5%288%29-13%5C%5C%26%20%3D40-13%5C%5C%26%20%3D27%5Cend%7Baligned%7D)
Therefore, x = 8 and the measure of each side is 27 units.
If 2 parallel lines are cut by a transversal, then the alternate exterior angles are congruent. If 2 parallel lines are cut by a transversal, then the same side interior angles are supplementary. A line that intersects 2 coplanar lines at 2 different points.
Step-by-step explanation:
here,
x°+15°=5x°-41°[being vertically opposite angle]
15°+41°=5x°-x°
56°=4x°
![\frac{56 }{4x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B56%20%7D%7B4x%7D%20)
thus,x=14°
<h3>hence,the value of x is 14°.</h3><h2>I hope this will help you.</h2><h2>please mark my answer as BRAINLIEST if you liked it....</h2>
Add 7 to both sides
Y+7=3
Divide both sides by 3
Y+7/3=x
Switch sides
X=y+7/3
Step-by-step explanation:
A square prism is a cube. The equation that represents the volume of a cube is:
length*width*height
or, in your case, b*b*h
If you are talking about a square-based pyramid, then you use 1/3 * length * width * height or 1/3 * b * b * h. You can use the exponents where needed.