Angle ABD=(3x+12), angle BDE=(7x-32) find the measures of both angles

Mathematics

1 answer:

horsena [70]3 years ago

7 0

Answer:

72 = ABD

108 = BDE

Step-by-step explanation:

Are the angles supplementary? (Do they equal 180 degrees?)

If so, the equation would be:

(3x + 12) + (7x - 32) = 180

You would then solve for x:

1. Add Like Terms

10x - 20 = 180

2. Addition Prop. of Eq.

10x = 200

3. Division Prop. of Eq.

x = 20

With x, you would then find angle ABD and BDE

3(20) + 12 = ABD

60 + 12 = ABD

72 = ABD

7(20) - 32 = BDE

140 - 32 = BDE

108 = BDE

You'd then check your answer. Does 72 + 108 = 180?

Yes, it does.

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Rowena is proving that AD ≅ EB. Which statement does the ♣ represent in her proof?

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Using the ASA congruence theorem, the missing statement in her proof is: A. ΔACD ≅ ΔECB.

<h3>What is the ASA Congruence Theorem?</h3>

Two triangles are congruent by the ASA congruence theorem if they have two pairs of corresponding congruent angles and a pair of included congruent sides.

In the proof given in the diagram, using the ASA congruence theorem, Rowena has been able to prove that ΔACD and ΔECB have two pairs of corresponding congruent angles and a pair of included congruent sides.

Therefore, the missing statement in her proof is: A. ΔACD ≅ ΔECB.

Learn more about the ASA congruence theorem on:

brainly.com/question/2102943

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