Together, the measures of ∠B , ∠C , and ∠D equal 180° . The angles have the following measures: m∠B=25° , m∠C=(3x)° , and m∠D=(3x+5)° . What are the measures of ∠C and ∠D ?
Since the sum of the measures of angles B, C, and D equal 180°, we can write the equation: 25° + (3x)° + (3x + 5)° = 180°.
Combining like terms, we get: 31° + 6x° = 180°.
Subtracting 31° from both sides, we have: 6x° = 149°.
Dividing both sides by 6, we find that x = 24.83°.
Therefore, ∠C = (3x)° = 3 * 24.83° ≈ 74.50°.
And ∠D = (3x + 5)° = 3 * 24.83° + 5° = 74.50° + 5° = 79.50°.
Thus, ∠C ≈ 74.50° and ∠D ≈ 79.50°.
you did it wrong.
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Apologies for the mistake.
Let's try again.
Given that the sum of angles B, C, and D is equal to 180°, we have:
∠B + ∠C + ∠D = 180°
Substituting the values we have:
25° + (3x)° + (3x + 5)° = 180°
Combining like terms:
25° + 3x° + 3x° + 5° = 180°
Simplifying:
8x + 30 = 180
Subtracting 30 from both sides:
8x = 150
Dividing both sides by 8:
x = 18.75
Therefore, ∠C = 3x° = 3 * 18.75° = 56.25°
And ∠D = 3x + 5° = 3 * 18.75° + 5° = 56.25° + 5° = 61.25°
So, the measures of ∠C and ∠D are 56.25° and 61.25°, respectively.
wrong again
Apologies for the mistake.
Let's try again.
Given that the sum of angles B, C, and D is equal to 180°, we have:
∠B + ∠C + ∠D = 180°
Substituting the values we have:
25° + (3x)° + (3x + 5)° = 180°
Combining like terms:
25° + 3x° + 3x° + 5° = 180°
Simplifying:
6x + 30 = 180
Subtracting 30 from both sides:
6x = 150
Dividing both sides by 6:
x = 25
Therefore, ∠C = 3x° = 3 * 25° = 75°
And ∠D = 3x + 5° = 3 * 25° + 5° = 75° + 5° = 80°
So, the measures of ∠C and ∠D are 75° and 80°, respectively.