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2 years ago

What is the missing reason for the 4th step in the proof below?

Mathematics

1 answer:

e-lub [12.9K]2 years ago

6 0

The reason for step 4 that is missing is: definition of linear pair.

<h3>What is a Linear Pair of a Straight Line Angle?</h3>

A line pair are two angles on a straight line whose sum equals 180 degrees.

Angles ANV and ANR line on a straight line and are therefore linear pair. This implies that:

m∠ANV + m∠ANR = 180 degrees

Therefore, the missing reason is: definition of linear pair.

Learn more about linear pair on:

brainly.com/question/13218054

#SPJ1

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2 years ago

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3 years ago

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3 years ago

Which of the following represent the values of x, y, and z.

Paraphin [41]

Answer:

Part 1) $z=4\sqrt{3}\ units$

Part 2) $y=4\sqrt{2}\ units$

Part 3) $x=4\sqrt{6}\ units$

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

<em>Find the value of z</em>

In the right triangle DBC

$cos(C)=\frac{4}{z}$ ----> equation A

In the right triangle ABC

$cos(C)=\frac{z}{12}$ ----> equation B

equate equation A and equation B

$\frac{4}{z}=\frac{z}{12}$

$z^{2}=48$

$z=4\sqrt{3}\ units$

step 2

In the right triangle DBC

Applying the Pythagoras Theorem

$z^{2}=y^{2}+4^{2}$

we have

$z=4\sqrt{3}\ units$

substitute

$(4\sqrt{3})^{2}=y^{2}+4^{2}$

$48=y^{2}+16$

$y^{2}=48-16$

$y^{2}=32$

$y=4\sqrt{2}\ units$

step 3

Find the value of x

In the right triangle ABC

Applying the Pythagoras Theorem

$12^{2}=x^{2}+z^{2}$

we have

$z=4\sqrt{3}\ units$

substitute

$12^{2}=x^{2}+(4\sqrt{3})^{2}$

$144=x^{2}+48$

$x^{2}=144-48$

$x^{2}=96$

$x=4\sqrt{6}\ units$

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3 years ago