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
(9x + 4)° + 32° = 90°
9x + 36° = 90°
9x = 54°
x=6
Practice 2-5
Proving Angles Congruent
Find the values of the variables.
4x + 1 = 65°
4x = 64
4y + 6y = 90
x = 16
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
and
mA = ¼mB
mA = ¼(144)
mB = 180
mA = 36°
mB = 144°
9.  A is five times as large as its complement,  B.
mA + mB = 90
and
mA = 5mB
mA = 5(15)
5mB + mB = 90
6mB = 90
mB = 15°
mA = 75°
10.  A is one eighth as large as its complement,  B.
mA + mB = 90
1/
8mB
+ mB = 90
9/
8mB
= 90
mB = 80°
and
mA = 1/₈ mB
mA = 1/₈(80)
mA = 10°
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°.
⇒ Def. of Supplementary s
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 ,
⇒ (Theorem 2-4) All right s are congruent.
2) mBOC + mCOD = 90,
⇒ Def. of Complementary s
3) mAOC + mCOE = 180, ⇒ Def. of Supplementary s
mAOB + mBOE = 180,
⇒ Def. of Supplementary s
mAOD + mDOE = 180,
⇒ Def. of Supplementary s
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