Find the measure of the unknown angles and sides of the given parallelogram as shown in the figure below:

Rectangle PSAL has a diagonal mPA = 5x - 14 cm and mLS = 4x + 6 cm

Solution:

mPA = mLS

5x - 14 = 4x + 6

5x - 4x = 6 + 14

x = 20

• x = 20

mPA = 5x - 14

mPA = 5(20) - 14

mPA = 100 - 14

mPA = 86 cm

• mPA = 86 cm

mPM = mPA/2

mPM = 86/2

mPM = 43 cm

• mPM = 43 cm

mSL = mLS = 4x + 6

mSL = 4x + 6

mSL = 4(20) + 6

mSL = 80 + 6

mSL = 86

• mSL = 86

Answer:

1.) mPM = 43 cm

2.) mSL = 86

Rhombus SAMT with m∠STM = (3x + 11)°

Solution:

m∠STM = (3x + 11)

Since there is only one given equation, which is 3x + 11,

Assuming triangle TSM is an equilateral triangle  from triangle STM

m∠STM = (3x + 11)

m∠STM = 3(49/3) + 11

m∠STM = 49 +11

m∠STM = 60°

• m∠STM = 60°

m∠MTA = m∠STM/2

m∠MTA = 60/2

m∠MTA = 30°

• m∠MTA = 30°

m∠TSA = 60 + 60

m∠TSA = 120°

• m∠TSA = 120°

m∠TSM = m∠TSA /2

m∠TSM = 120/2

m∠TSM = 60°

• m∠TSM = 60°

Answer:

3.) m∠MTA = 30°

4.) m∠TSM = 60°

Square FGHI

Solution:

m∠IFG = 90°

• m∠IFG = 90°

m∠JFG = m∠IFG/2

m∠JFG = 90/2

m∠JFG = 45°

• m∠JFG = 45°

Answer:

5.) m∠JFG = 45°

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