Answer:
x = 4
Step-by-step explanation:
An exterior angle of a triangle is equal to the sum of the remote interior angles.
18x +5 = (46) +(-1 +8x)
10x = 40 . . . . . . . . . . . . . subtract (5+8x) from both sides, simplify
x = 4 . . . . . . divide by 10
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<em>Additional comment</em>
The exterior angle is (18)(4) +5 = 77°. The marked unknown interior angle is -1+(8)(4) = 31°. The sum of the two remote interior angles is 46°+31° = 77°. The unmarked interior angle is 180°-77° = 103°.
Luckily for us, the diagram already divided this figure into separate polygons. What I will be explaining is basically the addition of the areas of all the separate polygons. The area of the uppermost triangle is:
1/2 x b x h
= 1/2 x 20 x 8
(the base is 20, because in a parallelogram, opposite sides are congruent)
=10 x 8
= 80 in. squared
The next polygon we will be taking the area of is the parallelogram with the base length of 20 and the height of 16.
Area = b x h
= 20 x 16
= 320 in. squared
Now all we have left to do is add the two areas to obtain the total area.
Total Area = 320 + 80 = 400 in. squared
Have a nice day hope this helps
Answer:
Q.5 ab=cd
Q.6 ad=bc
Q.7 ce=ae
Q.8 eb=ed
Q.9 angle D=angle B (opposite angle of parallelogram are equal)
let other angle of parallelogram be x.
angle A+angle B +angle C + angle D= 360° (sum of quadrilateral is 360°)
x+130°+x+130°=360°
2x+260°=360°
2x=360°-260°
2x=100°
x=100/2
x=50°
Q.10 similarly, angle b= angle d
let other angle be x.
x+61°+ x+61°=360°
2x+122°=360°
2x=360°+122°
2x=238°
x=238°/2
x=119°
Q.11 in quadrilateral opposite angles are equal and opposite angle of parallelogram are equal.
Q.12 in quadrilateral opposite angle are equal and opposite angle of parallelogram are equal.
Q.13 in quadrilateral opposite sides are equal and opposite sides are parellel and this property is also present in parallelogram.
q.14 in quadrilateral diagonal bisected each other and diagonal of parallelogram also bisect each other.
Y = 7x^2-3
x=7y^2-3
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