Question

in the following figures, solve for x. complete parts (a) through (c) below.
a.
figure a: intersecting lines with a 50° angle, a 75° angle, and x
b.
figure b: intersecting lines with a right angle, 7x, and 2x
a. solve for x.
x = 25°
(simplify your answer)
b. solve for x.
x = \\(\square\\)°
(simplify your answer)

Explanation:

Part (a)

Step1: Identify angle relationship

The sum of angles in a triangle (or using vertical/alternate angles) gives \( x + 50^\circ=75^\circ \) (since they are related by angle properties).

Step2: Solve for \( x \)

Subtract \( 50^\circ \) from both sides: \( x = 75^\circ - 50^\circ \)
\( x = 25^\circ \)

Part (b)

Step1: Identify angle sum

The angles \( 7x \), \( 2x \), and the right angle (\( 90^\circ \)) sum to \( 180^\circ \) (straight line). So \( 7x + 2x+ 90^\circ=180^\circ \)

Step2: Combine like terms

\( 9x + 90^\circ=180^\circ \)

Step3: Subtract \( 90^\circ \)

\( 9x = 180^\circ - 90^\circ \)
\( 9x = 90^\circ \)

Step4: Divide by 9

\( x=\frac{90^\circ}{9} \)
\( x = 10^\circ \)

Answer:

s:
a. \( x = 25^\circ \)
b. \( x = 10^\circ \)