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Scilla [17]
3 years ago
5

Why must angle A be 135°

Mathematics
1 answer:
Troyanec [42]3 years ago
4 0

Answer:

Because a is the measure of the interior angle of a regular octagon.

Step-by-step explanation:

Given figure is of a regular octagon.

Measure of one interior angle of regular octagon is given as:

a =  \frac{(n - 2) \times 180 \degree}{n}   \\  \\  =  \frac{(8 - 2) \times 180 \degree}{8}  \\  \\  =  \frac{6 \times180 \degree }{8}  \\  \\  =  \frac{1080 \degree}{8}  \\  \\   \huge \red{ \boxed{a= 135 \degree}}

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Answer:

30°

Step-by-step explanation:

First we must know that the sum of the interior angles of a triangle sum up to 180°.  Furthermore, a straight line is also 180°.  By using these what we know we can determine what the value of m∠X is.

First we know that m∠W and m∠Z make up a straight line, since m∠W is 105° it follows that:

180° = m∠W + m∠Z

And so:

m∠Z = 180° - m∠W = 180°-105° = 75°

m∠Z = 75°

Now, we also know that the sum of m∠X + m∠Y + m∠Z = 180° and so:

m∠X = 180° - m∠Y - m∠Z

m∠X = 180° - 75° - 75° = 30°

Therefore, m∠X = 30°


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Step-by-step explanation:

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