Answer:
Option B
The measure of angle b is 75°
Step-by-step explanation:
Method 1
we know that
In a inscribed quadrilateral, the opposite angles are supplementary
so
∠a+60°=180° ------> equation A
∠b+105°=180° -----> equation B
To find the measure of angle b solve the equation B
∠b+105°=180°
Subtract 105° both sides
∠b+105°-105°=180°-105°
∠b=75°
Method 2
see the attached figure with letters to better understand the problem
we know that
The inscribed angle measures half that of the arc comprising
so
∠105°=(1/2)[arc ADC]
arc ADC=2*105°=210°
<em><u>Find the measure of arc ABC</u></em>
we know that
arc ABC+arc ADC=360° -----> by complete circle
arc ABC=360°-210°=150°
<u><em>Find the measure of inscribed angle b</em></u>
∠b=(1/2)[arc ABC]
substitute
∠b=(1/2)[arc 150°]=75°
Answer:
C
Step-by-step explanation:
From the given coordinates
A(6, 0), B(0, 0) then AB = 6 - 0 = 6
B(0, 0), C(0, 8) then BC = 8 - 0 = 8
To calculate AC use Pythagoras' theorem on the right triangle formed
AC² = AB² + BC² = 6² + 8² = 36 + 64 = 100
Take the square root of both sides, hence
AC = = 10
Perimeter = AB + BC + AC = 6 + 8 + 10 = 24 → C
Answer:
Step-by-step explanation:
A quadratic equation in one variable given by the general expression:
Where:
The roots of this equation can be found using the quadratic formula, which is given by:
So:
As you can see, in this case:
Using the quadratic formula:
Therefore, the answer is: