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Iteru [2.4K]
3 years ago
7

a trapezoid has base lengths of (6x-1) units and 3 units. Its midsegment has a length of (5x-3) units. What is the value of x?

Mathematics
1 answer:
vodka [1.7K]3 years ago
3 0
1. You have that:

 - The<span> lengths of the bases are (6x-1) units and 3 units.
 - The midsegment has a length of (5x-3) units.

 2. To solve this exercise, you must apply the formula for calculate the length of the midsegment of a trapezoid, which is shown below:

 Midsegment=Base1+Base2/2

 As you can see, the midsegment is half the sum of the bases of the trapezoid.

 3. When you substitute the values, you obtain:

 (5x-3)=[(6x-1)+3]/2

 4. Now, you can solve the problem by clearing the "x":
</span>
 (5x-3)=[(6x-1)+3]/2
 2(5x-3)=6x-1+3
 10x-6=6x+2
 10x-6x=2+6
 4x=8
 x=8/4
 x=2
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\large{ \tt{☄ANSWERS \: +   \: REASONS}} :

  • \large{ \tt{ \angle \: 7 =  \boxed{ \tt{38 \degree}}}} \: ( \text{Being \: alternate \: angles)}

  • \large{ \tt{38 \degree + \angle 4 = 180 \degree}}( \text{Sum \: of \: co - interior \: angles}

\:  \:  \:  \:  \:  \large{ \tt{ ↦\angle \: 4 = 180 \degree - 38 \degree  =  \boxed{ \tt{142 \degree}}}}

  • \large{ \tt{ \angle \: 1 =  \angle \: 4 =   \boxed{ \tt{142 \degree}( \text{Being  \: vertical \: angles)}}}}

  • \large{ \tt{ \angle \: 8 =  \angle \: 4 =  \boxed{ \tt{142 \degree} \text{(Being \: corresponding \: angles)}}}}

  • \large{ \tt{ \angle \: 6 =  \angle \: 1 =  \boxed{  \tt{142 \degree} \text{(Being \:corresponding \: angles) }}}}

  • \large {\tt{  \angle \: 2 = \boxed{\tt{38 \degree}}\text{(Being \: corresponding \: angles)}}}

  • \large{ \tt{ \angle \: 3 = \boxed{\tt{38 \degree} }\text{(Being \: alternate \: angles)}}}

\large{ \tt{✺ \: TIPS} }:

  • If you have planned for study at 8:00 and now it's 8:05 then don't wait for 9 : 00 , Start studying that subject right now ! ♪

\large{ \tt{❃ \: LEARN \: ABOUT \: ALTERNATE \: , CORRESPONDING\:AND \: CO - INTERIOR \: ANGLES}} :

  • brainly.com/question/17147541

ツ Hope I helped! ♡

☼ Have a wonderful day / evening ! ☃

# StayInAndExplore ! ☂

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