Please answer this correctly without making mistakes I want helping hand people to answer this

k = 6

Step-by-step explanation:

Since the figures are similar, we can use ratios to solve

4         28

=

k         42

Using cross products

4 * 42 = 28k

Divide each side by 28

4*42/28 = 28k/28

6 = k

k = 6mm

Step-by-step explanation:

The shapes are similar, which means that each side on the triangle is proportionally similar to its corresponding side on the other triangle.

We can use proportions to solve for k:

4 and k are proportionally similar and 28 and 42 are proportionally similar.

You can then cross-multiply to get this:

28k = 168

k = 6

The missing side is 6 mm long.

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°

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x