Answer:
m∠B = 157°
Step-by-step explanation:
Cyclic quadrilateral is the quadrilateral whose vertices lie on the edge of the circle
In the cyclic quadrilateral each two opposite angles are supplementary (the sum of their measures is 180°)
∵ Quadrilateral ABCD is inscribed in a circle
- That means its four vertices lie on the edge of the circle
∴ ABCD is a cyclic quadrilateral
<em>Each two opposite angles in the cyclic quadrilateral are supplementary (The sum of their measures is 180°)</em>
∵ ∠B and ∠D are opposite angles in the quadrilateral ABCD
∴ m∠B + m∠D = 180° ⇒ opposite ∠s in a cyclic quadrilateral
∵ m∠B = (6x + 19)°
∵ m∠D = x°
- Substitute them in the rule above
∴ (6x + 19) + x = 180
- Add the like terms in the left hand side
∴ (6x + x) + 19 = 180
∴ 7x + 19 = 180
- Subtract 19 from both sides
∴ 7x = 161
- Divide both sides by 7
∴ x = 23
<em>Substitute the value of x in the expression of the measure of ∠B to find its measure</em>
∵ m∠B = 6(23) + 19
∴ m∠B = 138 + 19
∴ m∠B = 157°
Answer:
m∠P = 107º
Step-by-step explanation:
Since two sides are parallel this is a trapezoid
In a trapezoid, the angles on the same leg (called adjacent angles) are supplementary, meaning they add up to 180 degrees.
(7x + 31) + (21x - 19) = 180
combine like terms
28x + 12 = 180
Subtract 12 from both sides
28x = 168
Divide both sidees by 28
x = 6
m∠P = 21x - 19
m∠P = 21(6) - 19
m∠P = 107º
Answer: I think it would of be U: Axis
V:2
S: 4
T: 1
U: 2
R: Axis
Q: 3
P: Axis
Answer:
117.57 degrees
Step-by-step explanation:
Took the quiz hope this helps :)
