The weight of every type a widget is the same, the weight of every type b widget is the same, and the weight of every type c widget is the same. if the weight of 8 type a widgets is equal to the weight of 3 type b widgets, and the weight of 5 type b widgets is equal to the weight of 7 type c widgets. what is the ratio of the total weight of 1 type a widget and 1 type b widget, to the total weight of 1 type b widget and 1 type c widget?

Step-by-step explanation:

Given

weight of 8 Type A widget is equal to weight of 3 type B widgets

i.e. 8A=3B  (Let's say)

Also

Weight of 5 Type B widgets is equal to the weight of 7 type C widgets

i.e.

5B=7C

ratio of total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget

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°