Question

explain 5b bisecting angles
visit bim.easyaccessmaterials.com, read integrated mathematics 1 lesson 8.5, then read the section below.
example 5 - using a bisector to find angle measures
$overline{qr}$ bisects $\angle pqs$. find $m\angle pqr$ and $m\angle pqs$.
solution
step 1: because $overline{qr}$ bisects $\angle pqs$, $m\angle pqr = m\angle sqr$.
$m\angle pqr = m\angle sqr$ write the definition of an angle bisector.
$(4x - 10)\degree = (-3x + 130)\degree$ substitute angle measures.
$7x - 10 = 130$
$7x = 140$
$x = 20$
step 2: evaluate the expression for $m\angle pqr$ when $x = 20$.
$m\angle pqr = (4x - 10)\degree$
$= 4(20) - 10$
$= 70$
step 3: use the angle addition postulate to find $m\angle pqs$.
$m\angle pqs = m\angle pqr + m\angle sqr$
$= 70\degree + 70\degree$
$= 140\degree$
so, $m\angle pqr = 70\degree$ and $m\angle pqs = 140$
visit www.bigideasmathvideos.com to watch the flipped video instruction for the \try this\ problem(s) below.
try this video for extra example 5 - using a bisector to find angle measures

1. $overline{vb}$ bisects $\angle avc$, and $m\angle avc = 158\degree$. find $m\angle bvc$.

Explanation:

Step1: Apply angle bisector definition

An angle bisector splits an angle into two equal parts, so $m\angle BVC = \frac{1}{2}m\angle AVC$.

Step2: Substitute given angle measure

Substitute $m\angle AVC = 158^\circ$ into the formula:
$m\angle BVC = \frac{1}{2} \times 158^\circ$

Step3: Calculate the final value

$m\angle BVC = 79^\circ$

Answer:

$79^\circ$