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1 year ago

Find the measure of angle b

Mathematics

2 answers:

olga2289 [7]1 year ago

7 0

Answer:

b = 65 degrees

Step-by-step explanation:

As we can see, the line that angle b and 115 deg correspond to is a straight line. A straight line always measures at 180 deg.

Because of this principle, we know that:

$115+ b = 180$

We can simplify this one variable equation now:

$b=180-115\\$

Now solve:

$b=65$

And this makes sense. Just by eyeballing the angle, we can see that it is under 90 degrees.

So, b = 65 degrees

garik1379 [7]1 year ago

3 0

Answer:

Step-by-step explanation:

angles are on a straight line = sum of 180°, to find the value of "b" subtract the known angle (115°) from 180°

180 - 115 = 65°

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snow_tiger [21]

Answer:

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Step-by-step explanation:

(1) As definition, the area ( $A$ ) of a circle is calculated by:

$A = \pi$ x $r^{2}$ with $r$ is radius of circle.

(2) The relation between radius ( $r$ ) and diameter ( $d_{1}$ ) of a circle is:

$d_{1}$ = 2 x $r$

(3) Applying the Pythagorean theorem for a square with sides of length $x$ ,

the relation between side $x$ and diagonal $d_{2}$ is:

$x^{2} +x^{2} = d^{2} \\or\\2x^{2} = d^{2}$

=> The diagonal ( $d_{2}$ ) of that square is calculated by:

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(4) The square fits exactly inside a circle, with each of its vertices being on the circumference of the circle.

Applying the theorem of inscribed angle in a circle, the measure of arc BD is twice as the measure of inscribed angle BAD.

In other words, the measure of arc AC = 2 x 90 = 180 deg, or half of circle.

It means that the diagonal BD is coincide with a diameter of circle.

=> $d_{1} = d_{2}$

or $2$ x $r$ = $x\sqrt{2}$

or $r$ = $x\frac{\sqrt{2} }{2}$

Substitute $r$ back into original formula used for calculating the area of circle:

=> A = $\pi$ x $(x\frac{\sqrt{2}}{2})^{2}$ = $\pi$ x $\frac{x^{2}}{2}$

=> $x^{2} = A$ x $\frac{2}{\pi }$

=> $x = \sqrt{A}$ x $\sqrt{\frac{2}{\pi } }$ = $\sqrt{56}$ x $\sqrt{\frac{2}{\pi } }$ = 5.97 cm

Hope this helps!

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