Question

Geometry how do I do this help please number 5 and 3

Answer 1

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