Practice 2-5 (DNG page 283)
Proving Angles Congruent
Find the values of the variables.
(6y 10)° + (6y+10)° = 180°
12y = 180
y = 15
3x 40 = 2x - 10
-2x +40 = -2x +40
x = 30
(4z 10)° + z° = 90°
5z 10 = 90
5z = 100
z = 20
Practice 2-5
Proving Angles Congruent
Find the values of the variables.
4y + 6y = 90
10y = 90
y=9
Find the measure of each angle.
7. A is three times as large as its supplement, B.
mA + mB = 180
3mB + mB = 180
4mB = 180
mB = 45°
and mA = 3mB
mA = 3 (45° )
mA = 135°
Practice 2-5
Proving Angles Congruent
Find the measure of each angle.
8. A is one fourth as large as its supplement, B.
mA + mB = 180
¼ mB + mB = 180
5/
4
mB = 180
mB = 144°
and
mA = ¼mB
mA = ¼(144)
mA = 36°
9.  A is five times as large as its complement,  B.
10.  A is one eighth as large as its complement,  B.
Practice 2-5
Proving Angles Congruent
Write three conclusions that can be drawn from each figure.
55
125
55
1) mPMQ = 125° ,
⇒ Vertical s Theorem
2) mPMO = 55° ,
⇒ Def. of Supplementary s
3) mQMN = 55°.
 ???
Practice 2-5
Proving Angles Congruent
Write three conclusions that can be drawn from each figure.
Given (marked):
BOC ≅ COD
BOD is a right angle.
COE is a right angle.
1) BOD ≅ COE ,
 ???
2) mBOC + mCOD = 90,
 ???
3) mAOC + mCOE = 180,
 ???
mAOB + mBOE = 180,
 ???
mAOD + mDOE = 180,
 ???
Practice 2-5
Proving Angles Congruent
Write three conclusions that can be drawn from each figure.
BWC ≅ DWC,
⇒Given (marked)
1) mAWB + mBWC = 180,
⇒Def. of Supplementary s
2) mAWD + mDWC = 180,
⇒Def. of Supplementary s
3) AWB ≅ AWD ,
⇒Congruent Supplements Theorem