Quadrilateral ABCD is inscribed in this circle.

Mathematics

1 answer:

Sedbober [7]3 years ago

4 0

The answer to this is 65.

Remember that the angles opposite of each other equal to 180. So a+c=180 and b+d=180.

First, we solve for x. Since we know that b and d equal to 180, we subtract 148 from 180.
180-148=32. x=32.

Then we plug that in the expression for angle a.
2x+1 becomes 2(32)+1
2*32=64
64+1=65.
a=65

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What is the answer lol somebody help me please and thank you !

PilotLPTM [1.2K]

I'm guessing that you know about 45-45-90 and 30-60-90 triangles.

In 45-45-90 triangles, the legs are in a ratio such that the hypotenuse is $\sqrt{2}$ times the legs.

In 30-60-90 triangles, the legs are in a ratio of 1: $\sqrt{3}$ :2

In the picture given we have been given a value of the side of the 45-45-90 triangle. We can deduce that the value of the hypotenuse is 9 $\sqrt{2}$ because of the ratio of the sides of a 45-45-90 triangle.

The 30-60-90 triangle shares the same hypotenuse, and so we now know a value of one of its sides as well. The ratio of the side of value 'x' and the hypotenuse is $\sqrt{3}$ : 2

We can create an equation to solve for x using these ratios:

$\frac{\sqrt{3} }{2}$ = $\frac{x}{9\sqrt{2} }$