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Find the measures of HAB and CAB

Find the measures of HAB and CAB-example-1

1 Answer

5 votes

Answer:

<HAB = 48° and <CAB = 72°

Explanation:

Looking at the graph these two angles (<FAD = 20° and <DAH = ?) are complementary which means those two angles add up to 90°

Solve for <DAH.

<FAD = 20° + <DAH = ? = 90

Subtract <FAD = 20° to both sides leaving <DAH = ?

<DAH = 70°

Now that we have that angle we can solve for measured angles <HAB and <CAB. These three angles add up to 180°

<DAH + <HAB + <CAB = 180

Plug in our variables.

70° + 2x + 3x = 180°

Solve our x.

(2x + 3x) = 180° - 70°

5x = 120°

x = 24°

Now substitute x into the x to have our measured angle <HAB and <CAB.

<HAB = 2x = 2*24° = 48°

<HAB = 48°

<CAB = 3x = 3*24 = 72°

<CAB = 72°

User Marat Dukhan
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