The larger of 2 numbers is 8 more than twice the smaller. the sum of the number is 10 less than 3 times the larger . find the numbers

larger no =4, samller no=-2

Step-by-step explanation:

let , samller no=x, larger no=y

ac/ques, y=2x+8(1)

x+y=3y-10(2)

y=2x+8  put in equ (2)

x+2x+8=3(2x+8)-10

3x+8=6x+24-10

3x=-6

x=-2

x=-2 put in equ (1)

y=-4+8=4

larger no =y=4, samller no=x=-2

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°

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.