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castortr0y [4]
3 years ago
5

Two angles are complementary. The measure of ∠ABC is x° and the measure of ∠DBC is (3x + 10)°. What is the value of x?

Mathematics
2 answers:
serg [7]3 years ago
5 0
X+3x+10=90
4x=90-10
4x=80
x=20
Licemer1 [7]3 years ago
3 0

Answer: x = 20

Step-by-step explanation:

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Answer:

Part 1) x=16\ units

Part 2) x=23\ units

Part 3) AE=20\ units

Part 4) x= 6.25\ units

Part 5) x=26.67\ in

Step-by-step explanation:

Part 1) we know that

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In this problem

\frac{12}{3}=\frac{x}{4}\\\\3x=12*4\\ \\x=48/3\\ \\x=16\ units

Part 2) we know that

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the ratio of their corresponding sides are equal

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In this problem

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Part 3) we know that

If two triangles are similar

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the ratio of their corresponding sides are equal

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In this problem

\frac{AB}{CD}=\frac{AE}{ED}

substitute the values

\frac{10}{4}=\frac{2x+10}{x+3}

2.5(x+3)=2x+10

2.5x+7.5=2x+10

2.5x-2x=10-7.5

0.5x=2.5

x=5\ units

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Part 4) we know that

If two triangles are similar

then

the ratio of their corresponding sides are equal

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In this problem

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If two triangles are similar

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the ratio of their corresponding sides are equal

so

In this problem

\frac{30}{x}=\frac{45}{40}\\ \\45x=30*40\\ \\x=1,200/45\\ \\ x=26.67\ in



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Step-by-step explanation:

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