Question

QUICK PLZZ!!! If m<ABD = 71°, what are m<ABC and m<DBC?​

Answer 1

The measure of the angle

m ∠ ABC = 35°

m ∠ DBC = 36°

As per given information,

m ∠ ABD = 71°

m ∠ ABC = (7x - 7)

m ∠ DBC = (5x + 6)

From the diagram, we can say that,

m∠ABD = m∠ABC + m∠DBC

71 = (7x - 7) + (5x + 6)

71 = 12x - 7 +6

71 = 12x - 1

71 + 1 = 12x

72 = 12 x

Dividing both sides by 12 we get the value of x as

6 = x

So, by putting the value of x in the m∠ABC and m∠DBC we get the numerical value

m ∠ ABC = (7x - 7)

m ∠ ABC = 7 (6) - 7

m ∠ ABC = 42 - 7

m ∠ ABC = 35°

m ∠ DBC = (5x + 6)

m ∠ DBC = 5(6) + 6

m ∠ DBC = 30 + 6

m ∠ DBC = 36°

Question:-

If m∠ABD=71°, what are m∠ABC and m∠DBC?

Answer 2

m<ABC = 45

m<DBC = 34°

Step-by-step explanation:

Given:

m<ABD = 79°

m<ABC = (8x - 3)°

m<DBC = (5x + 4)°

Step 1: Generate an equation to find the value of x

m<ABC + m<DBC = m<ABD (angle addition postulate)

(8x - 3) + (5x + 4) = 79

Solve for x

8x - 3 + 5x + 4 = 79

13x + 1 = 79

Subtract 1 from both sides

13x + 1 - 1 = 79 - 1

13x = 78

Divide both sides by 13

x = 6

Step 2: find m<ABC and m<DBC by plugging the value of x into the expression of each angle

m<ABC = (8x - 3)°

m<ABC = 8(6) - 3 = 48 - 3 = 45°

m<DBC = (5x + 4)°

m<DBC = 5(6) + 4 = 30 + 4 = 34°

Explanation:

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