Which of the following sets of numbers could be the lengths of the sides of a triangle? a. 2, 4, 6 b. 4, 8, 2 c. 8, 3, 6 d. 12, 8, 3

Answer is C. 8, 3, 6

To answer this, you must know the Triangle Inequality Theorem.

The two shortest sides when added together, must be greater than the longest side.

A. 2 + 4= 6 which can't work since it equals the longest side of 6

B. 4 +2=6 The sum would be less than 8, which doesn't work

C. 6 +3 = 9 the sum is greater than 8, which makes it a triangle

D. 3 +8 = 11 11 is less than 12

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°