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The figure shows adjacent angles BAC and CAD. (attached figure)
Adjacent angles BAC and CAD sharing common ray AC

Given:
m∠BAD = 113°
m∠BAC = (3x −12)°
m∠CAD = (4x 20)°

Part A: Using the angle addition postulate, write and solve an equation for x. Show all your work.

Part B: Find the m∠CAD. Show all your work.

The figure shows adjacent angles BAC and CAD attached figure Adjacent angles BAC and CAD sharing common ray AC Given mBAD 113 mBAC 3x 12 mCAD 4x 20 Part A Using class=


Answer :

Intriguing456

Answer:

A)   [tex](3x-12)\° + (4x+20)\° = 113\°[/tex]

B)   [tex]x=35[/tex]

Step-by-step explanation:

The angle addition postulate tells us that the sum of the measures of adjacent angles equals the measure of the larger angle that they form.

Therefore:

  • [tex]m\angle BAC + m\angle CAD = m\angle BAD[/tex]

We can now plug in the given angle measures to solve for x:

[tex](3x-12)\° + (4x+20)\° = 113\°[/tex]

↓ canceling degrees on both sides

[tex]3x-12 + 4x+20 = 113[/tex]

↓ combining like terms

[tex]7x + 8 = 113[/tex]

↓ subtracting 8 from both sides

[tex]7x = 105[/tex]

↓ dividing both sides by 7

[tex]\boxed{x = 35}[/tex]

View image Intriguing456

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