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sashaice [31]
2 years ago
11

Solve for X, 132 is an exterior angle. Show work please!

Mathematics
2 answers:
Darina [25.2K]2 years ago
6 0

Answer:

105/9

Step-by-step explanation:

180 - 132 = 48 degrees

180 - 48 - 45

= 180 - 93

= 87 degrees

<2 = 180 - 87

= 93 degrees

=> 9x - 12 = 93

=> 9x = 105

=> x = 105/9

ruslelena [56]2 years ago
4 0

Answer:

x = 12°

m∠2 = 96°

Find the missing inside angle for right triangle:

180° - 132°

48°

Find the missing angle for left triangle:

90° - 48°

42°

As it is an isosceles triangle, the angles will be similar.

Thus solve:

9x - 12 + 42° + 42° = 180°

9x + 72° = 180°

9x = 180° - 72°

9x = 108°

x = 108°/9

x = 12°

Therefore m∠2 :

m∠2 = 9x - 12

m∠2 = 9(12) - 12

m∠2 = 96°

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Answer both with STEPS
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Answer:

7 )

x =  \frac{3\sqrt{2} }{2}

y= 3

8 )

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Step-by-step explanation:

7  )                                 8)

In Δ ABC                                      In Δ XYZ            

∠ C = 45°                                          ∠ X = 60°

∠ A = 90°                                           ∠ Y = 90°

AC= \frac{3\sqrt{2} }{2}             XY= 3\sqrt{6}

To Find :

x = ?

y = ?

Solution:

We Know

In Δ ABC

∠ C = 45°

∠ A = 90°

∴ ∠ B = 45°  ......Angle sum property of a triangle i.e 180°

∴  Δ ABC is an Isosceles Triangle

∴ AC = AB = x =  \frac{3\sqrt{2} }{2}

Now appplying Trignometry identity we get

\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\sin 45 = \frac{AC}{BC}\\\\\frac{1}{\sqrt{2} } =\frac{\frac{3\sqrt{2} }{2}}{y}\\\\y=\frac{3\times \sqrt{2}\times \sqrt{2}  }{2}\\\\y= 3

Now In Δ XYZ

∠ X = 60°

∠ Y = 90°

∴∠ Z = 30°  . .....Angle sum property of a triangle i.e 180°

Now appplying Trignometry identity we get

\tan X = \frac{\textrm{side opposite to angle X}}{\textrm{side adjacent to angle X}}

\tan 60 = \frac{YZ}{XY}\\\\\sqrt{3} =\frac{y}{3\sqrt{6} }\\  y= 3\sqrt{3} \sqrt{6} \\y= 9\sqrt{2}

Now,

\sin X = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\\\sin 60 = \frac{YZ}{XZ}\\ \\\frac{\sqrt{3} }{2} =\frac{9\sqrt{2} }{x} \\\\x=\frac{18\sqrt{2} }{\sqrt{3} } \\\textrm{after fationalizing the denominator root 3 we get}\\\\x=6\sqrt{6}

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4 0
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