Answer: x is 9° , y is 21°. The measure of angle ABE is 48°.
Step-by-step explanation:
First we will solve for x.
The variable x appears in the angle 8x + 18 and that angle is a right angle.
Right angles have the measure of 90 degrees so we will set the angle equal 90 and solve for x.
8x + 18 = 90 Subtract 18 from both sides
- 18 -18
8x = 72 divide both sides by 8
x = 9
y is also on the right side and the combination of both angles has to also equal 90 degrees because they form a right angle.
Since we already know x is 9 we will input it into the left side for x and solve for y.
y + 3(9) + 2y = 90
3y + 27= 90
-27 -27
3y = 63
y = 21
Now we need to find the measure of angle ABE.
ABE is represented by y + 3x so since we know the value of y and x we will input it into the expression and solve for the angle.
21 + 3(9) = m∠ABE
21 + 27= m∠ABE
48 = m∠ABE
This means the measure of angle ABE is 48°
Answer:
∠DEA=∠BAC
Step-by-step explanation:
∠DAE=∠BCA (corresponding angles)
Angles in a triangle add up to 180:
Angles in ΔDAE=Angles in ΔABC
∠DAE+∠EDA+∠DEA=∠BCA+∠ABC+∠BAC
∠EDA+∠DEA=∠ABC+∠BAC (since ∠DAE=∠BCA, we can cancel them out)
∠DEA=∠BAC (∠EDA=∠ABC=90)
10.5/7 is all you would need to do to find your answer of 1.5 yards of ribbon per bow.
8/6 4/3+4/3, 16/12 8/6+8/6 , 20/15 16/12 + 4/3