What are the square roots of 64144?
2 answers:
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Answer:
m∠R = 112°
m∠S = 112°
m∠T = 68°
Step-by-step explanation:
Quadrilateral QRST is a cyclic quadrilateral.
A <u>cyclic quadrilateral</u> is a quadrilateral drawn inside a circle where every vertex touches the circumference of the circle.
The <u>opposite angles</u> in a cyclic quadrilateral sum to 180°.
⇒ m∠Q + m∠S = 180°
⇒ m∠R + m∠T = 180°
Given:
- m∠Q = 68°
- m∠R = (3x + 40)°
- m∠T = (5x - 52)°
<u>Measure of angle Q</u>
⇒ m∠Q + m∠S = 180°
⇒ 68° + m∠S = 180°
⇒ m∠S = 180° - 68°
⇒ m∠S = 112°
<u>Measure of angles R and T</u>
⇒ m∠R + m∠T = 180°
⇒ (3x + 40)° + (5x - 52)° = 180°
⇒ )8x -12)° = 180°
⇒ 8x° = 192°
⇒ x = 24
Substituting the found value of x into the expressions for angles R and T:
⇒ m∠R = (3(24) + 40)°
⇒ m∠R = 112°
⇒ m∠T = (5x - 52)°
⇒ m∠T = 68°
Answer:
The length of the diagonal HJ is 10.82 units
Step-by-step explanation:
* Lets revise the rule of the distance between two points
- , where
and
are the two points
* Lets use this rule to find the length of the diagonal HJ
∵ The coordinates of point H are (-4 , 3)
∵ The coordinates of point J are (5 , -3)
∴ and
∴ and
- Lets find the length of the diagonal HJ by using the rule above
∴ HJ =
∴ HJ =
∴ HJ = 10.82
* The length of the diagonal HJ is 10.82 units