If x=1/3 y, show y=135°. Supplementary angle

see explanation

Step-by-step explanation:

Supplementary angles sum to 180°  , then

x + y = 180 , that is

y + y = 180 ( multiply through by 3 to clear the fraction )

y + 3y = 540

4y = 540 ( divide both sides by 4 )

y = 135°

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 first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8