Question

example 2 - finding angle measures
a) ∠1 is a complement of ∠2, and ( mangle 2 = 32^circ ). find ( mangle 1 ).
draw a diagram to illustrate the relationship.
( mangle 1 + mangle 2 = 90^circ ) write definition of complementary angles.
( mangle 1 + 32^circ = 90^circ ) substitute angle measures.
( mangle 1 = 58^circ ) subtract ( 32^circ ) from both sides.
so, ( mangle 1 = 58^circ ).
b) ∠3 is a supplement of ∠4, and ( mangle 3 = 148^circ ). find ( mangle 4 ).
draw a diagram to illustrate the relationship.
( mangle 3 + mangle 4 = 180^circ ) write definition of supplementary angles.
( 148^circ + mangle 4 = 180^circ ) substitute angle measures.
( mangle 4 = 32^circ ) subtract ( 148^circ ) from both sides.
so, ( mangle 4 = 32^circ ).
visit www.bigideasmathvideos.com to watch the flipped video instruction for the \try this\ problem(s) below.
try this video for extra example 2 - finding angle measures

1. ∠5 is a complement of ∠6, and ( mangle 6 = 53^circ ). find ( mangle 5 ).
2. ∠7 is a supplement of ∠8, and ( mangle 7 = 29^circ ). find ( mangle 8 ).

integrated math 1 b credit 1

Explanation:

Step1: (For 1) Define complementary angles

$m\angle5 + m\angle6 = 90^\circ$

Step2: (For 1) Substitute given angle measure

$m\angle5 + 53^\circ = 90^\circ$

Step3: (For 1) Solve for $m\angle5$

$m\angle5 = 90^\circ - 53^\circ = 37^\circ$

Step4: (For 2) Define supplementary angles

$m\angle7 + m\angle8 = 180^\circ$

Step5: (For 2) Substitute given angle measure

$29^\circ + m\angle8 = 180^\circ$

Step6: (For 2) Solve for $m\angle8$

$m\angle8 = 180^\circ - 29^\circ = 151^\circ$

Answer:

1. $m\angle5 = 37^\circ$
2. $m\angle8 = 151^\circ$