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joe's mom is 2 less than 3 times joe's age. if
his mom is 31, write an equation to find out how
old joe is.

Step-by-step explanation:

x = the mom...y = joe

x = 3y - 2

x = 31

31 = 3y - 2

31 + 2 = 3y

33 = 3y

33/3 = y

11 = y <=== joe is 11

after simplifying it i got: -36.25 as my answer. hope that !

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°