1. What is the measure of ∠ABC?

∠ ABC = 55°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ ABD is an exterior angle of the triangle , then

6x + 5 = x + 45 + 3x

6x + 5 = 4x + 45 ( subtract 4x from both sides )

2x + 5 = 45 ( subtract 5 from both sides )

2x = 40 ( divide both sides by 2 )

x = 20

Then

∠ ABD = 6x + 5 = 6(20) + 5 = 120 + 5 = 125°

∠ ABD and ∠ ABC are adjacent angles and are supplementary, thus

∠ ABC = 180° - ∠ ABD = 180° - 125° = 55°

x = 15

Step-by-step explanation:

given that y varies directly with x

mathematically we can express this as

y = k x , where k is a constant

step 1: find k

given x = 3 and y = 21

y = k x

21 = k (3)

k = 7

hence the equation becomes

y = 7 x

when y = 105,

105 = 7x

x = 105 / 7 = 15