Question

1. solve for x and y.

(diagram of two intersecting lines with angles x°, y°, and 25°)
x = _____
y = _____

1. which of the following is the measure of an acute angle?

a) 15° b) 90°
c) 125° d) 180°

1. solve for x.

(diagram of a triangle with angles x°, x°, and (2x)°)
x = _____

1. find the perimeter.

(diagram of a hexagon with side lengths 12, 7, 7, 12, 6, 6)
perimeter = _____

1. two angles that add up to 180° are called ______ angles.
2. solve for x.

(diagram of a right triangle with a supplementary angle of 150° and angle x°)
x = _____

Explanation:

Question 25

Step1: Identify vertical and supplementary angles

Vertical angles are equal, so \( x = 25^\circ \). Supplementary angles add to \( 180^\circ \), so \( y + 25^\circ = 180^\circ \).

Step2: Solve for \( y \)

\( y = 180^\circ - 25^\circ = 155^\circ \)

An acute angle is less than \( 90^\circ \). \( 15^\circ < 90^\circ \), \( 90^\circ \) is right, \( 125^\circ \) and \( 180^\circ \) are obtuse/straight.

Step1: Sum of triangle angles is \( 180^\circ \)

So \( x + x + 2x = 180^\circ \).

Step2: Combine like terms

\( 4x = 180^\circ \).

Step3: Solve for \( x \)

\( x = \frac{180^\circ}{4} = 45^\circ \)

Answer:

\( x = 25^\circ \), \( y = 155^\circ \)

Question 26