<CAT AND <MAN ARE VERTICAL ANGLES, WITH M<CAT=4(X+3) AND M<MAN =3(2X-3). WHAT ISTHE m<CAT

Question

<cat and <man are vertical angles, with m<cat= 4(x+3) and m<man= 3(2x-3). Whatis the M<cat?

Answer 1

Hi Diane!

Vertical angles are equal, so m∠CAT = m∠MAN

m∠CAT = 4(x+3)

m∠MAN = 3(2x-3)

m∠CAT = m∠MAN

4(x+3) = 3(2x-3)

4x+12 = 6x - 9 (multiply through parentheses)

-4x -4x (subtract 4x from both sides)

------------------

12 = 2x - 9

+9 +9 (add 9 to both sides)

--------------

21 = 2x

--- --- (divide both sides by 2)

2 2

21

--- = x

2

They're asking for the measure of

angle CAT (m∠CAT)

m∠CAT = 4(x+3)

21 3

= 4 ( -- + -- ) substitute 21/2 for x

2 1

21 3 2

= 4 ( --- + --- *--- ) get common denominator of 2

2 1 2

21 6

= 4 (---- + ---)

2 2

27

= 4( ---- )

2

27

= 2 4( ----) 4 divided by 2 is 2

2

= 2 (27)

= 54

The measure of ∠CAT = 54°