Question

In this figure, DC is parallel to AB. angle DCA is 3x+14, angle ACB is 10x+12, and angle CAB is 5x-2. Find the degrees in angle CBA.

Answer 1

Answer:

Angle CBA = 50 degrees

Step-by-step explanation:

Known Information:

• DC is parallel to AB
• Angles DCA and CAB are equal (they are alternate interior angles)
• Angles CAB + ACB + CBA = 180°

Calculations:

• $3x + 14 = 5x - 2$
• $16 = 2x$

• $x = 8$

• $180 - CAB - ACB = CBA$

• $180 - [ 5(8) - 2] - [ 10(8) + 12] = CBA$

• $100- [38] - [92] = CAB$

• $CBA = 50$

Answer 2

The measure of the angle CBA is 50 degrees if DC is parallel to AB. angle DCA is 3x+14.

What is an angle?

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have:

DC is parallel to AB. angle DCA is 3x+14, angle ACB is 10x+12, and angle CAB is 5x-2.

The equation can be framed:

3x + 14 = 5x - 2

x = 8

Angle CBA = 180 - (Angle CAB - Angle ACB)

Angle CBA = 180 - [5(8)-2+10(8)+12]

Angle CBA = 180 - [40-2+80+12]

Angle CBA = 180 - [40-2+80+12]

Angle CBA = 50

Thus, the measure of the angle CBA is 50 degrees if DC is parallel to AB. angle DCA is 3x+14.

Learn more about the angle here:

brainly.com/question/7116550

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