a. 180 degrees
b. 180 degrees
c. transitive property
d. m<3
e. m<3
Supplementary angles are angles that equal 180 degrees.
Transitive property : if two angles (segment) are each congruent to a third segment (angle) then they are both congruent to each other.
I can’t understand why everyone complicates this question. It can be easily solved by similar triangles.
In this png, we have something to make sure.
∠B=∠DAB
∠
B
=
∠
D
A
B
(Yes, dab)
This also means AD=BD
A
D
=
B
D
.
This is our basic construction of D, which is going to help us.
∠ADC=∠DAB+∠B=2∠B=∠CAB
∠
A
D
C
=
∠
D
A
B
+
∠
B
=
2
∠
B
=
∠
C
A
B
∠CAD=∠CAB−∠DAB=∠B
∠
C
A
D
=
∠
C
A
B
−
∠
D
A
B
=
∠
B
These are based on the fact that ∠A=2×∠B
∠
A
=
2
×
∠
B
Actually these conditions suffice. Because I am just proving that △ACD∼△BCA
△
A
C
D
∼
△
B
C
A
Similarity makes us realize the following:
ACBC=ADAB
A
C
B
C
=
A
D
A
B
and
ACBC=CDAC
A
C
B
C
=
C
D
A
C
So
AC×AB=BC×AD
A
C
×
A
B
=
B
C
×
A
D
and
AC2=BC×CD
A
C
2
=
B
C
×
C
D
So
BC2=BC×(BD+CD)=BC×(AD+CD)
B
C
2
=
B
C
×
(
B
D
+
C
D
)
=
B
C
×
(
A
D
+
C
D
)
=AC×AB+AC2
=
A
C
×
A
B
+
A
C
2
Q.E.D.
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Answer:
Step-by-step explanation:
90x - 60y = 68.....multiply by -1
90x - 70y = 91
---------------------------
-90x + 60y = -68 (result of multiplying by -1)
90x - 70y = 91
---------------------------add
-10y = 23
y = -23/10 <===
90x - 60y = 68
90x - 60(-23/10) = 68
90x + 138 = 68
90x = 68 - 138
90x = - 70
x = -70/90
x = -7/9 <=====
Answer:
x = 6.
y = 6.7.
z = 13.4.
Step-by-step explanation:
The 2 triangles contained in the biggest one are similar, so:
x/12 = 3/x
x^2 = 36
x = 6.
Applying the Pythagoras theorem:
z^2 = 6^2 + 12^2
z^2 = 36 + 144 = 180
z = 13.4.
y^2 = x^2 + 3^2
= 36 + 9
= 45
y = 6.7
Answer:
a= -12
Step-by-step explanation:
because
