Question

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

Answer 1

c. x = 76, y = 63, z = 104

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°

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Answer 2

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° .