Please help I need help with #17, 19, and 21

Step-by-step explanation:

All the angles in a triangle have to add up to 180 degrees.

#17.)

45+50=95

180-95=85

x=85

#18.)

This one is a little different. The furthest two angles are complimentary which means that they add up to 180 degrees (a straight line.) Once you find the missing angle to that one, you can do the same thing as you did in #17.

180-118=62.

25+62=87

180-87=93

x=93

#21.)

For this one a slightly larger equation is needed. Since we don't have a definite number for the bottom left angle, we have to use x+2 as our number. We first have to find the bottom right angle though.

180-108=72

x+x+2+72=180

2x+74=180

2x=106

x=53

Answer

#17=85

#19=93

#21=53

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°

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step-by-step explanation: