Solve for x, y, and z in the figure below. 47° 58°
x
y° / 81°
zº
N
оа
Ob
Ос
x = 34, y = 99, z = 41
x = 41, y = 92, z = 41
x = 72, y = 61, z = 41
X = 63, y = 70, z = 41
Od

Applying the definition of the straight line angle and sum of triangle, the values of the variables in the figure are:

Recall:

Thus:

y° + 81° = 180° (angles on a straight line)

y° = 180° - 81°

y° = 99°

x° +  y° + 47° = 180° (sum of triangle)

x° + 99° + 47° = 180°

x° + 146° = 180°

x° = 180° - 146°

x° = 34°

z° + 81° + 58° = 180° (sum of triangle)

z° + 139° = 180°

z° = 180° - 139°

z° = 41°

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Option (A)

Step-by-step explanation:

From the given triangle in the picture,

∠y and the angle measuring 81° is a pair of supplementary angles (linear pair angles).

m∠y + 81° = 180°

m∠y  = 180° - 81°

        = 99°

By the property of a triangle,

x° + y° + 47° = 180°

x° + y° = 180° - 47°

x° + y° = 133°

For y = 99°

x° + 99° = 133°

x° = 133° - 99°

   = 34°

Similarly, z° + 58° + 81° = 180°

z° + 139° = 180°

z° = 180° - 139°

z° = 41°

Therefore, Option (A) will be the correct option.