Find two numbers knowing that there’s some is 100 and the difference of their squares Is 1,000

the two numbers are 55 and 45

Step-by-step explanation:

according to the question :-

=》x + y = 100 - ( equation 1 )

and

=》

=》

( by algebraic identity )

=》

=》

=》

so,

by using linear equations :-

x + y = 100

x - y = 10

adding both equations we get,

now, putting the value of x in equation 1

i hope it helped you....

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°