Draw an obtuse angle big. place a point p inside the angle. now construct perpendiculars from the point to both sides of the angle. which side is closer to point p?

I have drawn three obtuse angles showing three different positions.

then taken a point p inside it.

Now to draw perpendicular from a point to a given line

we draw a line parallel fom that point to that given line.

After that from that point we draw perpendicular to that line.

Now the question arises which side is closer to point p ,

The answer is if length of perpendicular from p to the line is longer that side is farther from the point p , and if the length of perpendicular is shorter then that that line is nearer to point P.

question:

could we have options?

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°