Question

topic 2: perpendicular bisectors & angle bisectors

1. find sr.

$10x - 3$
$3x + 39$

1. find $m\angle lmn$.

$(4x + 2)^\circ$
$(7x - 37)^\circ$

Explanation:

Problem 8: Find $SR$

Step1: Set segments equal (bisector property)

$10x - 3 = 3x + 39$

Step2: Solve for $x$

$10x - 3x = 39 + 39$
$7x = 42$
$x = 6$

Step3: Substitute $x$ into $SR$

$SR = 3x + 39 = 3(6) + 39$

Problem 9: Find $m\angle LMN$

Step1: Set angles equal (bisector property)

$4x + 2 = 7x - 37$

Step2: Solve for $x$

$2 + 37 = 7x - 4x$
$39 = 3x$
$x = 13$

Step3: Calculate $\angle LMN$

$m\angle LMN = 2(4x + 2) = 2(4(13)+2)$

Answer:

Problem 8: $SR = 57$
Problem 9: $m\angle LMN = 108^\circ$