∠A and ∠B are vertical angles. If m∠A=(3x-30)° and m∠B=(2x-9)°,then find the value of x.

x = 21

Step-by-step explanation:

Vertical angles are congruent, thus

∠ A = ∠ B , substitute values

3x - 30 = 2x - 9 ( subtract 2x from both sides )

x - 30 = - 9 ( add 30 to both sides )

x = 21

Hello there! :)

Vertical angles are congruent, therefore:

∠A ≅ ∠B

3x - 30 = 2x - 9

Subtract 2x from both sides:

3x - 2x - 30 = 2x - 2x - 9

x - 30 = -9

Add 30 to both sides:

x - 30 + 30 = -9 + 30

x = 21.

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°

the ratio of balloons to tables is 5: 2 and the constant variation is 5.

the equation is y=5x