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masya89 [10]
3 years ago
11

Find the values of x,y,z. This diagram is not a scale.

Mathematics
2 answers:
never [62]3 years ago
5 0

Answer:

c. <em>x</em><em> </em>= 76, <em>y</em><em> </em>= 63, <em>z</em><em> </em>= 104

Step-by-step explanation:

First, you have to use the Interior Angles Theorem [m<1 + m<2 + m<3 = 180°] to find the m<x:

46° + 58° + 76° = 180°

Now that you have the m<x, to find the m<z, you have to use the Supplementary Angles Theorem, which states that two angles [in this case] add up to 180°:

76° + 104° = 180°

Finally, to find the m<y, you again have to use the Interior Angles Theorem:

13° + 63° + 104° = 180°

If you are ever in need of assistance, do not hesitate to let me know by subscribing to my You-Tube channel [USERNAME: MATHEMATICS WIZARD], and as always, I am joyous to assist anyone at any time.

Serjik [45]3 years ago
3 0

Important:
                             The sum of the three angles inside
                              every triangle is always 180°.


First, look at the left triangle alone.
Two of its angles are 46° and 58° .  (46° + 58° ) = 104°
That leaves (180° - 104° ) = 76° degrees for the third angle.
The third angle in that triangle is 'x'. 
                                                         x = 76° .

At the point where 'x' and 'z' come together:
'x' and 'z' are a "linear pair".
Placed side-by-side, they form a straight line.
So (x + z) = 180° .
But  x = 76°.
So z = (180° - 76°).              z = 104° .

Now look at the the skinny triangle on the right alone.
The angle at the top is 13°, and  z = 104°. 
(13° + 104°) = 117° . 
That leaves (180° - 117°) = 63° for the third angle.
'y' is the third angle.
                                                 y = 63° .

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Considering the given triangle XIF, to determine XI, we would apply the sine rule. It is expressed as

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