Question

this is a 2 - page document
use the diagram below to answer questions 1 and 2.
diagram: l---m---n

1. if ( lm = 22 ) and ( mn = 15 ), find ( ln ).
2. if ( ln = 54 ) and ( lm = 31 ), find ( mn ).

1. if ( rt = 36 ), find the value of ( x ).

diagram: r---( 6x + 1 )---s---( x + 7 )---t

1. if ( df = 9x - 39 ), find ( ef ).

diagram: d---47---e---( 3x + 10 )---f

1. if ( uw = 6x - 35 ), find ( uw ).

diagram: u---19---v---( 4x - 20 )---w

1. if ( hj = 7x - 27 ), find the value of ( x ).

diagram: h---( 3x - 5 )---i---( x - 1 )---j

1. if ( bd = 7x - 10 ), ( bc = 4x - 29 ), and ( cd = 5x - 9 ), find each value.

diagram: b---c---d
( x = _____ )
( bc = _____ )
( cd = _____ )
( bd = _____ )

1. if ( overline{bd} cong overline{bc} ), ( bd = 5x - 26 ), ( bc = 2x + 1 ), and ( ac = 43 ), find ( ab ).

diagram: a---b---c, b---d (vertical)

Explanation:

Question 1:

Step1: Identify segment addition.

Since \( L \), \( M \), \( N \) are collinear, \( LN = LM + MN \).

Step2: Substitute values.

Given \( LM = 22 \), \( MN = 15 \), so \( LN = 22 + 15 \).

Step1: Use segment addition.

\( LN = LM + MN \), so \( MN = LN - LM \).

Step2: Substitute values.

Given \( LN = 54 \), \( LM = 31 \), so \( MN = 54 - 31 \).

Step1: Segment addition for \( RT \).

\( RT = RS + ST \), so \( 36 = (6x + 1) + (x + 7) \).

Step2: Simplify equation.

Combine like terms: \( 36 = 7x + 8 \).

Step3: Solve for \( x \).

Subtract 8: \( 28 = 7x \), divide by 7: \( x = 4 \).

Answer:

\( LN = 37 \)

Question 2: