Since opposite angles of a cyclic quadrilateral are supplementary,
A= 180-101=79°
B= 180-68=112°
The measure of ∠BAF is 54°.
Solution:
DF and CE are intersecting lines.
m∠EAF = 72° and AB bisects ∠CAF.
∠EAF and ∠DAC are vertically opposite angles.
Vertical angle theorem:
<em>If two lines are intersecting, then vertically opposite angles are congruent.</em>
∠DAC ≅ ∠EAF
m∠DAC = 72°
<em>Sum of the adjacent angles in a straight line = 180°</em>
m∠DAE + m∠EAF = 180°
m∠DAE + 72° = 180°
Subtract 72° from both sides.
m∠DAE = 108°
∠CAF and ∠DAE are vertically opposite angles.
⇒ m∠CAF = m∠DAE
⇒ m∠CAF = 108°
AB bisects ∠CAF means ∠CAB = ∠BAF
m∠CAB + m∠BAF = 108°
m∠BAF + m∠BAF = 108°
2 m∠BAF = 108°
Divide by 2 on both sides, we get
m∠BAF = 54°
Hence the measure of ∠BAF is 54°.
Answer:
Step-by-step explanation:
1. Express each quadratic function f in the form f (x) -yo = p (x - xo) x ϵ R, where xo, i, p ϵ R are appropriately chosen. Indicate the coordinates
of the vertex of the parabola, the minimum or maximum of the function f, especially R. Draw the graph of f.
a) f (x) = 2x2 + 3x -5, ϵ R,
b) f (x) = -3x2 + 7x +9, ϵ R,
c) f (x) = - x +1, ϵ R,
HELP YOU GIVE YOU CORONA PLIS
Answer:
The required number of buses=340/52=85/13buses
Step-by-step explanation:
Combine the two equations in the right amounts to eliminate y :
-2 (2x + 3y) + (3x + 6y) = -2 (17) + 30
-4x - 6y + 3x + 6y = -34 + 30
-x = -4
x = 4
Solve for y :
2x + 3y = 17
8 + 3y = 17
3y = 9
y = 3
