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The figure shows adjacent angles BAC and CAD.

Adjacent angles BAC and CAD sharing common ray AC

Given:
m∠BAD = 134°
m∠BAC = (2x + 3)°
m∠CAD = (4x −1)°

Part A: Using the angle addition postulate, write and solve an equation for x. Show all your work. (6 points)

Part B: Find the m∠CAD. Show all your work. (4 points)



Answer :

ogorwyne

The equation for x is written as 134° = (2x + 3)° + (4x −1)°

The value of x = 22

The value of angle m∠CAD = 87 degrees

Given data:

m∠BAD = 134°

m∠BAC = (2x + 3)°

m∠CAD = (4x −1)°

Adjacent angles BAC and CAD

How to solve for x using the angle addition postulate

m∠BAD hosts the two angles such that the sum of the the two angles gives m∠BAD. Hence we solve as follows:

m∠BAD = m∠BAC + m∠CAD ( angle addition postulate )

134° = (2x + 3)° + (4x −1)°

134 = 2x  + 3 + 4x - 1

1354 = 2x + 4x + 3 - 1

134 = 6x + 2

6x = 134 - 2

6x = 132

x = 132 / 6

x = 22

How to find m∠CAD

m∠CAD = (4x −1)°

= 4x - 1

= 4 * 22 - 1

= 88 - 1

= 87 degrees

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