5-x= -(x - 5)
how many solutions does this equation have

Infinitely many solutions

Step-by-step explanation:

5-x= -(x - 5) ➡ 5 - x = -x + 5 add x to both sides and subtract 5 from both sides

5 - x - 5 + x = -x + x - 5 + 5 ➡0 = 0 in this case we say the equation has infinitely many solutions because whatever value you give for x there will always be a solution.

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°