∠1 and ∠2 are supplementary // given∠3 and ∠4 are supplementary // given∠1 ≅ ∠3 // given m∠1 + m∠2 = 180° // definition of supplementary anglesm∠3 + m∠4 = 180° // definition of supplementary angles m∠1 + m∠2 = m∠3 + m∠4 // transitive property of equality m∠1 = m∠3 // definition of congruent angles m∠1 + m∠2 = m∠1 + m∠4 // substitution property of equality (replaced m∠3 with m∠1) m∠2 = m∠4 // subtraction property of equality (subtracted m∠1 from both sides) ∠2 ≅ ∠4 // definition of congruent angles
Recall that
(x + y)² = x² + 2xy + y²
Then if x + y = √7 and x² + y² = 6, we have
(√7)² = 6 + 2xy ⇒ 2xy = 1
We also have
(x - y)² = x² - 2xy + y²
so that
(x - y)² = 6 - 1 ⇒ (x - y)² = 5
which means x - y has two possible values, √5 or -√5.
Answer:
137
Step-by-step explanation:
The sum of all three angles; <ABC, <ABD, and <CBD is equal to 360
now we know <ABC = 118 and
the measure of central angle <CBD is equal to measure of the arc it sees so it's = 105
we are asked to find the m<ABD
118 + 105 + <ABD = 360 add like terms
223 + <ABD = 360 subtract 223 from both sides
m<ABD = 137
Answer:
x = 14
y = 22
Step-by-step explanation:
y = x + 8
4x - 2y = -12
Solve
_____________
Since we see that the first equation has y alone, we can substitute it into the values of y in the second equation.
4x - 2(x + 8) = -12
Distribute :
4x - (2(x) + 2(8)) = -12
4x - 2x +16 = -12
Combine like terms :
2x + 16 = -12
Subtract 16 from both sides :
2x = -28
Divide 2 from both sides to get x alone :
x = 14
Now that we know what x is, substitute it in the first equation to get y :
y = (14) + 8
y = 22
