Question

∠abc is a straight angle.
find ( mangle abx ) and ( mangle cbx ).
diagram: a---b---c (straight line), with x above b. angle abx is ( (14x + 70)^circ ), angle cbx is ( (20x + 8)^circ )
( mangle abx = square^circ )
( mangle cbx = square^circ )

Explanation:

Step1: Set up the equation (straight angle is 180°)

Since \( \angle ABC \) is a straight angle, the sum of \( \angle ABX \) and \( \angle CBX \) is \( 180^\circ \). So we have the equation:
\( (14x + 70) + (20x + 8) = 180 \)

Step2: Solve for x

Combine like terms:
\( 14x + 20x + 70 + 8 = 180 \)
\( 34x + 78 = 180 \)
Subtract 78 from both sides:
\( 34x = 180 - 78 \)
\( 34x = 102 \)
Divide both sides by 34:
\( x = \frac{102}{34} = 3 \)

Step3: Find \( m\angle ABX \)

Substitute \( x = 3 \) into \( 14x + 70 \):
\( 14(3) + 70 = 42 + 70 = 112 \)

Step4: Find \( m\angle CBX \)

Substitute \( x = 3 \) into \( 20x + 8 \):
\( 20(3) + 8 = 60 + 8 = 68 \)

Answer:

\( m\angle ABX = 112^\circ \)
\( m\angle CBX = 68^\circ \)