Question

(SAT Prep) Find the value of x.

Answer 1

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Answer 2

The value of x is equal to 24°

Given:

Angles in the triangle are 94°, 41° and the angles in the bisecting line are ∠x and 111°

To Find:

The value of x.

Solution:

In a triangle, the angle sum property is 180°, which means that the three angles of a triangle when added together are equal to 180°.

Here we can see two triangles. Let us name the larger triangle XYZ and the smaller triangle STZ.

The angles are named ∠X = 94°, ∠Y = 41°, and ∠Z. From the small triangle its named as ∠S = x, ∠T = 111° and ∠Z/

Let us find the value of ∠Z through the angle sum property of ΔXYZ

∠X + ∠Y + ∠Z = 180°

Substitute the values,

94° + 41° + ∠Z = 180°

135° + ∠Z = 180°

∠Z = 180° - 135°

∠Z = 45°

Let us find the value of x by solving the angle sum property of ΔSTZ

∠S + ∠T + ∠Z = 180°

x + 111° + 45° = 180°

x + 156° = 180°

x = 180° - 156°

x = 24°

Therefore, the value of x is equal to 24°

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