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3 years ago

What is an angle that is supplementary KFA?

Mathematics

1 answer:

cestrela7 [59]3 years ago

6 0

Given:

A diagram.

To find:

An angle that is supplementary to ∠KFA.

Solution:

Supplementary angle: Two angles are called supplementary angles if they are lie on the same side of a straight line and their sum is 180 degrees.

From the given diagram, it is clear that ∠KFA lies on the intersection of lines HL and IK.

∠KFA and ∠DFA lie on the same side of a straight line IK.

∠KFA and ∠KFL lie on the same side of a straight line HL.

So, ∠DFA and ∠KFL are the angles supplementary to ∠KFA.

We need only one supplementary angle. So, we write either ∠DFA or ∠KFL.

Therefore, an angle that is supplementary to ∠KFA is ∠KFL.

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Answer:

Given :

ABC is a right triangle in which ∠ABC = 90°,

Also, Legs AB and CB are extended past point B to points D and E,

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$\angle EAC = \angle ACD = 90^{\circ}$

To prove :

$EB\times BD=AB\times BC$

Proof :

In triangles AEC and EBA,

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By AA similarity postulate,

$\triangle AEC \sim \triangle EBA$ ,

Similarly,

$\triangle AEC \sim \triangle ABC$

$\implies\triangle EBA\sim \triangle ABC-----(1)$

Now, In triangles ADC and CBD,

∠ACD = ∠CBD ( right angles )

∠ADC= ∠BDC ( common angles )

By AA similarity postulate,

$\triangle ADC \sim \triangle CBD$ ,

Similarly,

$\triangle ADC \sim \triangle ABC$

$\implies \triangle CBD\sim \triangle ABC-----(2)$

From equations (1) and (2),

$\triangle EBA\sim \triangle CBD$

The corresponding sides of similar triangles are in same proportion,

$\frac{EB}{BC}=\frac{AB}{BD}$

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3 years ago

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scoray [572]

Answer:

x = 6

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To find x we set up an equation as so:

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Then we solve by multiplying 4.5 by 8 and 6 by x

$6x=36$ Solve for x

$\frac{6x}{6} =\frac{36}{6}$ x = 6

To check our answer when we substitute x or 6 we divide to make sure both sides equal the same number

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