7) state the prime factorization of 30.

Step-by-step explanation:

We analyze between which prime numbers we can divide the number 30. The smallest prime number by which we divide is 2. Then:

We now look for the smallest prime number that divides the 15. Since 15 is not a multiple of 2, we make the division with the number 3 that is divisor of 15.

We now look for a number that divides to 5, but since 5 is a prime number, the only divisor other than 1 is 5. Then:

This ends the decomposition of 30 and we find 3 prime factors:

2,3 and 5.

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°