Step-by-step explanation:
Let a, b, c be the measures of the interior angles and x, y, z be the measures of the exterior angles of the triangle. Where x and adjacent to a, y is adjacent to b and z is adjacent to c.
By interior angle sum postulate of a triangle:
a + b + c = 180°... (1)
Therefore, by remote interior angle theorem:
x = b + c.... (2)
y = a + c..... (3)
z = a + b.... (4)
Adding equations (2), (3) & (4)
x + y + z = b + c + a + c + a + b
x + y + z = 2a + 2b + 2c
x + y + z = 2(a + b + c)... (5)
From equations (1) & (5)
Thus, the sum of exterior angles so formed is equal to four right angles.
Proved.
9514 1404 393
Answer:
- arc BC = 60°
- m∠ADC = 60°
- m∠AEB = 105°
- m∠ADP = 45°
- m∠P = 60°
Step-by-step explanation:
The sum of arcs of a circle is 360°. The given conditions tell us arc BC ≅ arc AB, so the four arcs of the circle have ratios ...
CB : BA : AD : DC = 2 : 2 : 3 : 5
The sum of ratio units is 2+2+3+5 = 12, so each one stands for 360°/12 = 30°. Then the arc lengths are ...
arc BC = arc BA = 60° . . . . 2 ratio units each
arc AD = 90° . . . . . . . . . . . . 3 ratio units
arc DC = 150° . . . . . . . . . . . .5 ratio units
The inscribed angles are half the measure of the intercepted arcs:
∠ADC = (1/2) arc AC = 1/2(120°) = 60°
∠ADP = 1/2 arc AD = 1/2(90°) = 45°
The angles at E are half the sum of the measures of the intercepted arcs.
∠AEB = (arc AB + arc CD)/2 = (60° +150°)/2 = 105°
Angle P is half the difference of the intercepted arcs.
∠P = (arc BD -arc AD)/2 = (210° -90°)/2 = 120°/2 = 60°
__
In summary, ...
arc BC = 60°
m∠ADC = 60°
m∠AEB = 105°
m∠ADP = 45°
m∠P = 60°
Answer:
The Answer is -467
Step-by-step explanation:
all it did was move the decimal to the right once
Answer:
your answer is correct
it's A
and don't worry didn't spam ya
Hello There!
x - 5 ≤ - 6
+ 5 + 5
x ≤ -1.
The answer is A.
Hope This Helps You!
Good Luck :)
