How many different triangles can be formed from four rods with lengths of 1 meter, 3 meters, 5 meters, and 7 meters?

Since there is no angle restriction in this case, therefore the one rule that is applicable to this is that in forming a triangle, the sum of the lengths of the two smaller sides (A + B) should be larger than the length of the biggest side (C):

Triangle length rule: Side A + Side B > Side C

We can see that no matter how we combine the rods, the only combination of rods that satisfies this rule is:

 Triangle formed by rods 3 meters, 5 meters, and 7 meters

Therefore, there is only 1 triangle that can be formed from these four rods.

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°

it is true

step-by-step explanation:

all the combinations add up i used   calculator