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3 years ago

Please help me! geometry question!

Mathematics

2 answers:

bogdanovich [222]3 years ago

8 0

40 degrees is the answer

Vinvika [58]3 years ago

7 0

Answer:

Step-by-step explanation:

<AOC = 108°

<AOB = 3x + 4°

<BOC = 8x - 28°

< AOB + <BOC = <AOC

3x + 4° + 8x - 28° = 108°

11x - 24° = 108°

11x = 108° + 24°

11x = 132°

x = 132° / 11

x = 12°

< AOB = 3 *12° + 4° = 40°

Hope it will help :)

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The coordinates of K are: $\mathbf{K = (12,12)}$
The coordinates of I are: $\mathbf{I = (24,24)}$
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The given parameters are:

$\mathbf{R =(24,0)}$

$\mathbf{N =(12,18)}$

$\mathbf{T =(12,6)}$

$\mathbf{E =(18,15)}$

K is the midpoint of N and T.

So, we have:

$\mathbf{K = (\frac{N_x + T_x}{2},\frac{N_y + T_y}{2})}$

This gives

$\mathbf{K = (\frac{12 + 12}{2},\frac{18+ 6}{2})}$

$\mathbf{K = (12,12)}$

E is the midpoint of T and I.

So, we have:

$\mathbf{E = (\frac{I_x + T_x}{2},\frac{I_y + T_y}{2})}$

This gives

$\mathbf{(18,15) = (\frac{I_x + 12}{2},\frac{I_y+ 6}{2})}$

Multiply through by 2

$\mathbf{(36,30) = (I_x + 12,I_y+ 6)}$

By comparison

$\mathbf{I_x + 12 = 36.\ I_y + 6 =30}$

So, we have:

$\mathbf{I_x= 24.\ I_y =24}$

Hence, the coordinates of I are:

$\mathbf{I = (24,24)}$

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So, we have:

$\mathbf{I = (\frac{E_x + B_x}{2},\frac{E_y + B_y}{2})}$

This gives

$\mathbf{(24,24) = (\frac{18 + B_x}{2},\frac{15 + B_y}{2})}$

Multiply through by 2

$\mathbf{(48,48) = (18 + B_x,15 + B_y)}$

By comparison

$\mathbf{18 + B_x = 48,\ 15 + B_y = 48 }$

So, we have:

$\mathbf{B_x = 30,\ B_y = 33 }$

Hence, the coordinates of B are:

$\mathbf{B = ( 30,33 )}$