Question

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Answer 1

Answer:

1) <DHG = 94 degrees

2) <3 = 29 degrees

3) <1 = 47 degrees

4) <5 = 78 degrees

5) <4 = 60 degrees

Step-by-step explanation:

1). 2a -3 = 4a -10 (vertical angles)

- 3 + 10 = 4a - 2a

7 = 2a

a = 7/2

<5 = 2(7/2) - 3 = 4 degrees and <3 = 4(7/2) - 10 = 4 degrees

<DHG = 90+4 = 94 degrees

2). 4p+5+2p+1 90 (complementary angles)

6p+6 = 90

6p = 90-6

p = 84/6

p = 14

<1 = 61 degrees and <5 = 29 degrees

<3 = 29 degrees

3). 4w - 13 + 2w + 18 = 90 (complementary angles)

6w + 6 =90

6w = 90-6

W = 14

m<BHC = 4(14) - 3 = 53 and m<DHC = 2(14)+19 = 47

<1 = 47 degrees

4). <1 = <4 (vertical angles)

2d+7=3d-15

7+15 = 3d-2d

d = 22

<1 = 2(22)+7=51 and <4 = 3(22)-15=51

<5 = 180 - 102 = 78 degrees

5). 5r + 20 + 3r = 180

8r = 180 - 20

r = 160/8

r = 20

<AHB = (3)(20) = 60

<AHF = 180-60 = 120

<AHG = 120/2 = 60

<AHG = <4 (vertical angles = 60 degrees