Mark, jessica, and nate each downloaded music from the same website. mark downloaded 10 songs in total consisting of pop, rock, and hip hop. jessica downloaded five times as many pop songs, twice as many rock, and three times as many hip hop songs as mark. she downloaded 28 songs total. if nate downloaded 20 songs total with three times as many pop songs, three times as many rock songs, and the same number of hip hop songs as mark, how many songs of each type did mark download

Mark downloaded 1 pop songs, 4 rock songs, and 5 hip hop songs.

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°

can you complete your sentence? i could !