Question

Could someone help me with this Geometry I'm stuck on x & y.

Answer 1

x=30 degrees, y=85 degrees

Explanation:

Assuming u know that z=75 degrees, we know that since lines xy and zw are parallel, we know that x=30 degrees, since we know x=30 and that z is a base angle of an isosceles triangle, we know y=180-z-x

Answer 2

• w = 105°
• x = 30°
• y = z = 75°

Explanation:

You want to know the measures of the marked angles in the given figure.

Parallel lines

The two lines are indicated as parallel, so alternate interior angles are congruent:

x ≅ 30°

y ≅ z

Isosceles triangle

Angle z is a base angle of the isosceles triangle with vertex angle 30°. Consequently, its measure is ...

z = (180° -30°)/2 = 75°

Linear pair

The angles z and w are a linear pair, so supplementary:

w = 180° -z = 180° -75° = 105°

The measures of the angles are ...

• w = 105°
• x = 30°
• y = z = 75°

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Additional comment

The relation for z comes from the fact that the sum of angles in a triangle is 180°, and the two base angles of an isosceles triangle have the same measure:

2z +30° = 180°

2z = 180° -30°

z = (180° -30°)/2

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