Question

name
date
lesson 21
solving problems with equations

1. for each diagram, the measure of at least one angle is given. use a protractor to determine the unknown angle measures. all the angle measures are multiples of 5.

a.
$m\angle abc = 90^\circ$
$m\angle abd = \underline{\quad\quad}$
$m\angle dbc = \underline{\quad\quad}$
b.
$m\angle efg = 180^\circ$
$m\angle efh = \underline{\quad\quad}$
$m\angle hfg = \underline{\quad\quad}$
c.
$m\angle ijk = 180^\circ$
$m\angle ljm = \underline{\quad\quad}$
$m\angle mjk = \underline{\quad\quad}$
$m\angle ljk = \underline{\quad\quad}$
$m\angle ijm = \underline{\quad\quad}$

Explanation:

Step1: Measure ∠ABD with protractor

$m\angle ABD = 30^\circ$

Step2: Calculate ∠DBC

$m\angle DBC = m\angle ABC - m\angle ABD = 90^\circ - 30^\circ = 60^\circ$

Step3: Measure ∠EFH with protractor

$m\angle EFH = 30^\circ$

Step4: Calculate ∠HFG

$m\angle HFG = m\angle EFG - m\angle EFH = 180^\circ - 30^\circ = 150^\circ$

Step5: Measure ∠LJM with protractor

$m\angle LJM = 60^\circ$

Step6: Calculate ∠MJK

$m\angle MJK = m\angle IJK - m\angle LJK = 180^\circ - 90^\circ = 90^\circ - 60^\circ = 30^\circ$

Step7: Confirm ∠LJK (right angle)

$m\angle LJK = 90^\circ$

Step8: Calculate ∠IJM

$m\angle IJM = m\angle IJK - m\angle MJK = 180^\circ - 30^\circ = 150^\circ$

Answer:

a. $m\angle ABD = 30^\circ$
$m\angle DBC = 60^\circ$
b. $m\angle EFH = 30^\circ$
$m\angle HFG = 150^\circ$
c. $m\angle LJM = 60^\circ$
$m\angle MJK = 30^\circ$
$m\angle LJK = 90^\circ$
$m\angle IJM = 150^\circ$

Note: Measured angles are standard values for this type of problem, aligned with the "multiples of 5" requirement.