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Wittaler [7]
1 year ago
13

Please help me geometry

Mathematics
1 answer:
Semenov [28]1 year ago
3 0
<h2>Answer :</h2>

\large \bf \implies \angle{BAC} = 40 \degree

<h2>Step-by-step explanation :</h2>

\bf \implies  \angle{ABC} + \angle{BAC} = 90\degree [The acute angles of a right triangle are complementary]

\bf \implies  50x + 40x = 90\degree

<u>Substitute</u> :

\angle{BAC} = 40x \:  \: , \:  \: \angle{ABC} = 50x  \: into \: \angle{ABC} + \angle{BAC} = 90\degree

  • \sf{x =  1}

<u>Calculate 50x + 40x = 90°</u> ↑

  • \sf{\angle{BAC} = 40}

Substitute x = 1 into \bf{\angle{BAC} = 40x} ↑

\boxed{ \bold{\angle{BAC} = 40} }\:  \mathfrak{ans.}

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Part (A)

We have n = 5 sides, so the measure of any exterior angle of a regular pentagon is E = 360/n = 360/5 = 72

Each interior angle is therefore 180-E = 180-72 = 108 degrees.

---------------

Alternatively, you could use the formula below with n = 5

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<h3>Answer: 108 degrees</h3>

====================================================

Part (B)

We're told that CDF is 70 degrees. From part (A) we know that angle CDE is 108 degrees, so this must mean that angle EDF is 108-70 = 38 degrees.

Similarly, angle FEA is 85 degrees, which subtracts from angle AED to get 108 - 85 = 23 degrees. This is the measure of angle DEF.

So far we found

angle EDF = 38

angle DEF = 23

Let's call these x and y for shorthand. Let z be the missing third angle of triangle DFE.

So,

x+y+z = 180

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61+z = 180

x = 180-61

x = 119

Interior angle DFE is 119 degrees.

Note how 90 < x < 180 showing we have an obtuse angle. It is not a reflex angle because the statement 180 < x < 360 is false.

So we subtract the value of x from 360

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---------------

<h3>Answer: 241 degrees</h3>
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