Answer:
x = 10°
Step-by-step explanation:
a). Since, opposite angles of a cyclic quadrilateral are supplementary angles"
Therefore, in cyclic quadrilateral ABDE,
m∠ABD + m∠AED = 180°
110° + m∠AED = 180°
m∠AED = 180° - 110°
= 70°
b). AD = ED [Given]
m∠EAD = m∠AED [Since, opposite angles of equal sides are equal in measure]
m∠EAD = m∠AED = 70°
By triangle sum theorem in ΔABD,
m∠BAD + m∠ABD + m∠ADB = 180°
m∠BAD + 110° + 40° = 180°
m∠BAD = 180 - 150
= 30°
m∠AEB = m∠AED + m∠DAB [By angles addition postulate]
m∠AEB = 70° + 30°
= 100°
By triangle sum theorem in the large triangle,
x° + m∠AEB + m∠EAB = 180°
x° + 100° + 70° = 180°
x = 180 - 170
x = 10°
Answer:
x=12
Step-by-step explanation:
16x - (8x + 6) =90
The first step is to distribute the - sign
16x -8x -6 =90
Now we combine the like terms
8x-6 = 90
Add 6 to each side
8x-6+6 = 90+6
8x = 96
Divide each side by 8
8x/8 = 96/8
x =12
Answer:
x = 8
y = 21
Step-by-step explanation:
(7x + 12)° and (12x - 28)° are alternate interior angles. Alternate interior angles are congruent. Therefore:
(7x + 12)° = (12x - 28)°
Solve for x
7x + 12 = 12x - 28
Collect like terms
7x - 12x = - 12 - 28
-5x = -40
Divide both sides by -5
-5x/-5 = -40/-5
x = 8
(12x - 28)° + (9y - 77)° = 180° (linear pair)
To find y, plug in the value for x = 8.
12(8) - 28 + 9y - 77 = 180
96 - 28 + 9y - 77 = 180
Combine like terms
- 9 + 9y = 180
Add 9 to both sides
-9 + 9y + 9 = 180 + 9
9y = 189
Divide both sides by 9
9y/9 = 189/9
y = 21
Answer:
the slope of 15 is more difficult to run on
Step-by-step explanation:
The larger the slope, the steeper the ramp. A slope of zero is a horizontal line, which would be relatively easy to run on. A slope of undefined is a wall, which we cannot run on (we would fall off). The larger the number, the steeper it gets
Answer:
495 in
Step-by-step explanation:
The formula for the volume of a triangular prism is V = 
· w · h · l, where w represents with, l represents length, and h represents height. Using this and plugging in the values, we can solve.
V = · 5 · 11 · 18
V = 2.5 · 11 · 18
V = 27.5 · 18
V = 495
hope this helps :)
