Find the length of the missing side
The length of the missing side is

52m

Step-by-step explanation:

as this is a right angled triangle (has a 90° angle), you can use the Pythagoras theorem to work out the missing side.

Pythagoras theorem:

side A squared (labeled on diagram below)

+ side B squared

= side C squared

for this example though, we don't know the length of side B so we need to swap around the formula.

replace the letters for their numbers,

(calculate)

2704 = b² but we want b by itself so we will square root b² (2704)

∴ side B = 52m (remember we were calculating in meters)

I hope this was helpful :-)

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°