11. If triangle ABC is an isosceles triangle and triangle DBE is an equilateral triangle, find each missing
2 answers:
Answer:
∠1 = 43°, ∠2 = 17°, ∠3 = 120°, ∠4 = ∠5 = ∠6 = 60°, ∠7 = 17°, ∠8 = 120°, ∠9 = 43°.
Step-by-step explanation:
I found the figure for this problem.
It is provided that ΔABC is isosceles and ΔDBE is equilateral.
Isosceles Triangle:
According to the definition the length of two sides are equal and hence the two base angles are equal.
Equilateral Triangle:
All the sides are of equal length and can also be defined as equiangular with all the angles of measure 60°
CALCULATION:
For any triangle the sum of interior angles is always 180°.
ΔABC: ∠1+ (∠2 + ∠5 + ∠7)+∠9= 180°,
where, (∠2 + ∠5 + ∠7) is the total angle ∠ABC
ΔABC is isosceles so,
∠1 = ∠9,
4x+3 = 9x-47,
50 = 5x ⇒ x=10,
Putting the value of x in ∠1 we get,
∠1 = 4*(10)+3 = 43°,
∠1 = 43°.
ΔABD: ∠1+ ∠2+∠3= 180°
Now in order to find ∠2, firstly we have to find ∠3 in ΔABD.
According to the exterior angle property, the exterior angle of an equilateral triangle is always 120°. Since ∠3 is an exterior angle for the equilateral triangle ΔDBE therefore,
∠3 = 120°,
furthermore,
∠2 = 180° - ∠3 - ∠1,
⇒ ∠2 = 180° - 120° - 43°
∠2 = 17°.
ΔDBE: ∠4+ ∠5+∠6= 180°,
Also, ΔDBE is equilateral ⇒ ∠4 = ∠5 = ∠6 = 60°.
Now from ∠1+ (∠2 + ∠5 + ∠7)+∠9= 180°
we can find ∠7,
⇒ ∠1+ (∠2 + ∠5 + ∠7)+∠9= 180°
∠7 = 180° - (∠2 + ∠5 + ∠1+∠9),
∠7 = 180° - (17° + 60° + 43° + 43°),
∠7 = 180° - (163°)
∠7 = 17°.
Similarly, ∠8 is an exterior angle for the equilateral triangle ΔDBE therefore,
∠8 = 120°,
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A,B,C,D i.e. all statements are true!
<u>Step-by-step explanation:</u>
According to question, Lynn works as a part-time vendor selling necklaces for $15 each and bangles for $10 each. She needs to earn a minimum of $300 per week to cover her expenses. The inequality for above scenario will be :
where, x is number of necklaces & y is number of bangles.
A.
Lynn will meet her goal if she sells 12 bangles and 12 necklaces. i.e. x=12 and y=12 , putting values inequality : which follows inequality . True statement!
B.
Lynn will meet her goal if she sells 20 bangles and 6 necklaces.
putting values inequality : which follows inequality . True statement!
C.
Lynn will meet her goal if she sells 6 bangles and 12 necklaces. putting values inequality : , which follows inequality . True statement!
D.
Lynn will meet her goal if she sells 2 bangles and 18 necklaces.putting values inequality : , which follows inequality . True statement!
Answer:
No, these triangles cannot lie on the same line.
Step-by-step explanation:
For two triangles to lie on the same line they must have the same slope.
The slope of the bigger triangle is
and the slope of the smaller triangle is
slopes are negative because the triangles are leaning to the left.
We see that the slopes of the two triangles are not the same; therefore, they cannot lie on the same line.