Answer:
A. 85°
Step-by-step explanation:
By intersecting chords theorem:
![m\angle ABC= \frac{1}{2} (130 \degree + 40 \degree)](https://tex.z-dn.net/?f=%20m%5Cangle%20ABC%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20%28130%20%5Cdegree%20%2B%2040%20%5Cdegree%29)
![m\angle ABC= \frac{1}{2}\times 170 \degree](https://tex.z-dn.net/?f=%20m%5Cangle%20ABC%3D%20%20%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20170%20%5Cdegree)
![m\angle ABC= 85 \degree](https://tex.z-dn.net/?f=%20m%5Cangle%20ABC%3D%20%2085%20%5Cdegree)
Answer:
<D = 100
<E =30
<F =50
Step-by-step explanation
Given that triangles triangle ABC and triangle DEF are similar, this means that their angles are congruent i.e
<A = <D
<B = <E
<C = <F
Given
<A = 100 then <D = 100
<B = 30°, then <E = 30°
To get <F, we will use the expression
<D+<E+<F = 180 (sum of angles in a triangle is 180°)
100+30+<F = 180
130+<F = 180
<F = 180-130
<F = 50°
Hence the measure of <F is 50°
Answer:
a) 10 inches
b) 48 feet
Step-by-step explanation:
10 inches, 60/6 = 10
48 feet, 8*6 = 48
Lets go step by step and factor out each as we go
first lets factor out a 3 since 3 is common in 9 and 3
3(3ab^2 - abc)
now lets factor out a since its common in both
3a(3b^2 - bc)
now lets factor out a b since its common in both
3ab(b - c)
we can't factor anything else out so we are done.
Answer:
x = -1
x = 3
Step-by-step explanation:
![\sf x^2 - 2x = 3](https://tex.z-dn.net/?f=%5Csf%20x%5E2%20-%202x%20%3D%203)
Add 1 to both sides:
![\sf \implies x^2 - 2x+1 = 3+1](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20x%5E2%20-%202x%2B1%20%3D%203%2B1)
Factor the left side:
![\sf \implies (x-1)^2 = 4](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20%28x-1%29%5E2%20%3D%204)
Square root both sides:
![\sf \implies x-1 = \pm2](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20x-1%20%3D%20%5Cpm2)
Therefore:
![\sf \implies x-1=-2 \implies x=-1](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20x-1%3D-2%20%5Cimplies%20x%3D-1)
![\sf \implies x-1=2 \implies x=3](https://tex.z-dn.net/?f=%5Csf%20%5Cimplies%20x-1%3D2%20%5Cimplies%20x%3D3)