Answer:
Question 3:
JK = 15 units
ML = 24 units
m∠L = 112°
m∠M = 46°
Step-by-step explanation:
Question 3:
In the kite the longest diagonal is the axis of symmetry of it
∵ JKLM is a kite
∵ KM is the longest diagonal
∴ KM is the axis of symmetry of kite JKLM
- That means it divides the kite into two congruent Δs
∴ Δs KJM and KLM are congruent
∴ JK = KL ⇒ from congruence
∴ JM = ML ⇒ from congruence
∴ m∠J = m∠L ⇒ from congruence
From the figure
∵ KL = 15 units ⇒ given
∴ JK = 15 units
∵ JM = 24 units ⇒ given
∴ ML = 24 units
∵ m∠J = 112° ⇒ given
∴ m∠L = 112°
∵ The kite is a quadrilateral
- The sum of the interior angle of any quadrilateral is 360°
∴ m∠J + m∠K + m∠L + m∠M = 360°
∵ m∠J = 112° ⇒ given
∵ m∠K = 90° ⇒ given
∵ m∠L = 112 ⇒ proved
- Substitute them in the equation above
∴ 112 + 90 + 112 + m∠M = 360
- Add the like terms
∴ 314 + m∠M = 360
- Subtract 314 from both sides
∴ m∠M = 46°
Question 5 has not enough information to solve
