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Scalene triangle labeled with A (degrees), B (degrees), C (degrees), and D (degrees). Do not scale it. Find the value of x if D=124, A=54, and B=8x+44. And no, it is not -5.25.

11 answers

In a triangle, the sum of the interior angles is always 180 degrees. Given the angles \(A\), \(B\), \(C\), and \(D\) in the scalene triangle, we can express this relation as:

\[ A + B + C = 180^\circ \]

However, since you specified that \(D\) is one of the angles, we should set up the equation as follows:

\[ A + B + D = 180^\circ \]

Substituting the given values into the equation, we have:

\[ 54 + (8x + 44) + 124 = 180 \]

Now, combine the known angles:

\[ 54 + 124 + 44 + 8x = 180 \]

Left side simplifies to:

\[ 222 + 8x = 180 \]

Next, isolate \(8x\) by subtracting 222 from both sides:

\[ 8x = 180 - 222 \]

\[ 8x = -42 \]

Now, divide both sides by 8:

\[ x = \frac{-42}{8} = -5.25 \]

It appears that this contradicts your statement that \(x\) is not -5.25. This indicates a misunderstanding of the problem, as the calculations are correct based on the provided measurements.

Since this result closely tied to your provided conditions, I would re-check if the angles provided add up correctly to the triangle properties as needed, or you may want to review the representation or values given. If the angles sum correctly, \(x\) indeed computes to \( -5.25 \).

Wrong

Let's go through the problem step-by-step carefully to determine \(x\) correctly.

Given:

  • \(D = 124^\circ\)
  • \(A = 54^\circ\)
  • \(B = 8x + 44\)

We know that the sum of the angles in a triangle is \(180^\circ\). Therefore, we can set up the following equation:

\[ A + B + D = 180^\circ \]

Substituting the known values into the equation:

\[ 54 + (8x + 44) + 124 = 180 \]

Now simplify the left-hand side:

\[ 54 + 44 + 124 + 8x = 180 \]

Calculating \(54 + 44 + 124\):

\[ 222 + 8x = 180 \]

Next, isolate \(8x\) by subtracting \(222\) from both sides:

\[ 8x = 180 - 222 \]

\[ 8x = -42 \]

Now, divide both sides by \(8\):

\[ x = \frac{-42}{8} = -5.25 \]

It seems the calculations confirm that \(x\) equals \(-5.25\). If this cannot be correct based on the conditions you've stated, I encourage you to verify the values of the angles or check if there was further context or constraints that could change the situation. Please provide additional details or clarify any requirements!

Try this one instead: A =53, B=5x+29, and C=26

Let's find the value of \(x\) given the angles in the triangle:

  • \(A = 53^\circ\)
  • \(B = 5x + 29^\circ\)
  • \(C = 26^\circ\)

According to the triangle angle sum property:

\[ A + B + C = 180^\circ \]

Substituting the known values:

\[ 53 + (5x + 29) + 26 = 180 \]

Combining the constants on the left side:

\[ 53 + 29 + 26 + 5x = 180 \]

Calculating \(53 + 29 + 26\):

\[ 108 + 5x = 180 \]

Next, isolate \(5x\) by subtracting \(108\) from both sides:

\[ 5x = 180 - 108 \]

\[ 5x = 72 \]

Now, divide both sides by \(5\):

\[ x = \frac{72}{5} = 14.4 \]

Thus, the value of \(x\) is \(14.4\).

Right triangle. Labeled A degrees and B degrees Find the value of x if A equals 3x+20 and B=1x

In a right triangle, one of the angles is \(90^\circ\). Therefore, the sum of the other two angles \(A\) and \(B\) must be \(90^\circ\).

Given:

  • \(A = 3x + 20^\circ\)
  • \(B = x^\circ\)

Since the sum of angles \(A\) and \(B\) in a right triangle equals \(90^\circ\), we can write the equation:

\[ A + B = 90^\circ \]

Substituting the expressions for \(A\) and \(B\):

\[ (3x + 20) + x = 90 \]

Now, combine like terms:

\[ 4x + 20 = 90 \]

Next, isolate \(4x\) by subtracting \(20\) from both sides:

\[ 4x = 90 - 20 \]

\[ 4x = 70 \]

Now, divide both sides by \(4\):

\[ x = \frac{70}{4} = 17.5 \]

Thus, the value of \(x\) is \(17.5\).

Right triangle. Labeled A degrees, C degrees, and B degrees. Find the value of B if C = 156

It seems there might be a misunderstanding in the context of a right triangle. In a right triangle:

  • One angle is always \(90^\circ\).
  • The sum of the other two angles \(A\) and \(B\) must equal \(90^\circ\).

If \(C = 156^\circ\), it can't be part of a right triangle because the angle \(C\) exceeds \(90^\circ\).

Please double-check the angles provided and ensure that they make sense in the context of a triangle. If you have two angles specified in a right triangle, typically, the third angle must also be calculated based on the triangle's properties. If you meant that angle \(C\) is either the hypotenuse angle (which can't be \(156^\circ\)) or a different triangle type, please clarify!

Find the value of B if C equals 156

If \(C = 156^\circ\), and we need to find the value of \(B\), we must determine the context. However, it is important to note that the sum of angles in a triangle is always \(180^\circ\).

For a triangle, we can write:

\[ A + B + C = 180^\circ \]

Substituting the value of \(C\) into the equation:

\[ A + B + 156 = 180 \]

Now, isolate \(A + B\) by subtracting \(156\) from both sides:

\[ A + B = 180 - 156 \]

\[ A + B = 24^\circ \]

Now, we cannot determine the exact value of \(B\) without knowing the value of \(A\). However, we can express \(B\) in terms of \(A\):

\[ B = 24 - A \]

If you have additional information about the angle \(A\) or the type of triangle, please provide it, and I can help find the exact value of \(B\).