Let jk be the median of lmba. find jk, m∠a and m∠alm

JK = 83 , m∠A = 70° , m∠ALM = 110°

Step-by-step explanation:

* Lets explain how to solve the problem

∵ ABCD is a trapezoid

∴ DC // AB

∴ m∠D + m∠A = 180° ⇒ interior supplementary angles

∵ m∠D = 110°

∴ 110° + m∠A = 180° ⇒ subtract 110° from both sides

∴ m∠A = 70°

∵ L is the midpoint of AD, and M is the midpoint of BC

∴ LM is the median of trapezoid ABCD

∴ LM // AB and DC

∴ m∠D = m∠ALM ⇒ corresponding angles

∵ m∠D = 110°

∴ m∠ ALM = 110°

- The length of the median is half the sum of the lengths of the two

 parallel bases

∴ LM = 1/2 (AB + DC)

∵ AB = 96 units and DC = 44 units

∴ LM = 1/2 (96 + 44) = 1/2 (140) = 70 units

- In the quadrilateral ABML

∵ AB // LM

∵ AL ≠ BM

∴ ABML is a trapezoid

∵ JK is its median

∴ JK = 1/2 (AB + LM)

∵ AB = 96 units ⇒ given

∵ LM = 70 units ⇒ proved

∴ JK = 1/2 (96 + 70) = 1/2 (166) = 83

∴ JK = 83 units

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)