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Mnenie [13.5K]
3 years ago
11

Help asap!!! Midterms

Mathematics
1 answer:
scoray [572]3 years ago
8 0

Answer:

The value of x is 5.

Step-by-step explanation:

Label the diagram such as

Given:

AD= x

DB= x +5

AE = x - 2

EC = x + 1

DE || BC

To Find:

x = ?

Solution:

Basic Proportionality Theorem:

"If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio".

DE || BC

∴ \dfrac{AD}{DB}= \dfrac{AE}{EC} ...Basic Proportionality Theorem

Substituting the values in it we get

\dfrac{x}{x+5}= \dfrac{x-2}{x+1}\\x(x+1)=(x+5)(x-2)\\\\x^{2}+x= x^{2}+3x-10\\  -2x=-10\\\\x=\dfrac{10}{2}=5\\ \\\therefore x =5

The value of x is 5.

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3 years ago
A and B are supplementary. A is 20 less than three times the measure of B. What are the measures of A and B?
Amanda [17]

Answer:

∠ A = 130° , ∠ B = 50°

Step-by-step explanation:

supplementary angles sum to 180°

express ∠ A in terms of ∠ B , that is ∠ A = 3∠B - 20 , then

∠ A + ∠ B = 180° , that is

3∠B - 20+ ∠B = 180 ( add 20 to both sides )

4∠B = 200 (divide both sides by 4 )

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3 years ago
Given the regular octagon, what is the length of any side?
Jlenok [28]

Answer:110

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so 15*5+35=75+35=110

3 0
3 years ago
Read 2 more answers
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