Pls help i’m so confused!!

Mathematics

1 answer:

pentagon [3]3 years ago

3 0

Answer:

11 units^2

Step-by-step explanation:

We know that the area of a square is the side squared, so we can use the inverse of this formula to say the side of a square is the square root of the the area. This gives us√33 and √44 as the side lengths of the red and green squares respectively. Next, we use the pythagorean theorem to find the other side of the white right triangle, which is also a side of the blue square. So:

(√44)^2 - (√33)^2 = side^2

44 - 33 = side

side^2 = 11

side = √11

To find the area of a square, you just square the side, so we get (√11)^2 which is just 11 units^2.

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#2 is the one I need help with

sleet_krkn [62]

Step-by-step explanation:

By arc sum Postulate of a circle:

2 x + 3x + 4x = 360°

9x = 360°

x = 360°/9

x = 40°

3x = 3* 40° = 120°

By inscribed angle theorem:

$m\angle 1= \frac {1}{2} \times 3x\\\\\therefore m\angle 1= \frac {1}{2} \times 120°\\\\\huge \red {\boxed {\therefore m\angle 1= 60°}}$

By tangent secant theorem:

$m\angle 2 = \frac {1}{2} \times 3x\\\\\therefore m\angle 2 = \frac {1}{2} \times 120°\\\\\huge \purple {\boxed {\therefore m\angle 2 = 60°}}$

Since, measure of central angle is equal to the measure of its corresponding minor arc.

$m\angle 3 = 3x\\\\\huge \pink {\boxed {\therefore m\angle 3 = 120°}}$

By angle sum Postulate of a triangle:

$m\angle 3 + 2 m\angle 4 = 180°\\\\120° + 2 m\angle 4 = 180° \\\\2 m\angle 4 = 180°- 120° \\\\2 m\angle 4 = 60° \\\\m\angle 4 = \frac {60°}{2} \\\\\huge \orange {\boxed {m\angle 4 =30°}}$