4
the diagram below, not drawn to scale, shows two triangles, jlk and mlp, with jk parallel to ml. lm = mp,
klp is a straight line e jlm = 22° and angle lmp-36°
144
360
calculate, giving reasons for your answers, the measure of each of the following:
i. zmlp
ii. zljk
iii. ljkl
iv. zklj

∠MLP = 72° ,           ∠LJK = 22° ,            ∠JKL = 72° ,          ∠KLJ  =  86°

Step-by-step explanation:

Here, given In ΔJLK and  ΔMLP

Here,  JK  II  ML,  LM = MP

∠JLM = 22° and  ∠LMP = 36°

Now, As angles opposite to equal sides are equal.

⇒ ∠MLP = ∠MPL  = x°

Now, in  ΔMLP

By ANGLE SUM PROPERTY:   ∠MLP + ∠MPL  + ∠LMP = 180°

⇒ x° + x° + 36° = 180°

⇒ 2 x  = 180 - 36 = 144

or, x  = 72°

⇒ ∠MLP = ∠MPL  = 72°

Now,as  JK  II  ML

⇒ ∠LJK = ∠JLM = 22° ( Alternate pair of angles)

Now, by the measure of straight angle:

∠MLP + ∠JLM + ∠JLK = 180°  ( Straight angle)

⇒ 72° + 22° + ∠JLK = 180°

or, ∠JLK  =  86°

In , in  ΔJLK

By ANGLE SUM PROPERTY:   ∠JKL + ∠JLK  + ∠LJK = 180°

⇒  ∠JKL + 86° + 22° = 180°

⇒ ∠JKL   = 180 - 108 = 72 , or ∠JKL = 72°

Hence, from  above proof ,  ∠MLP = 72° , ∠LJK = 22° , ∠JKL = 72° ,

∠KLJ  =  86°

x = 10.1

step-by-step explanation:

all of the angles of a tirangle add up to 180º

180 - 65 = 115 (since we already know the value of one angle)

(2x + 7) + (8x + 7) = 115

(combins like terms) 10x + 14 = 115

(isolate the variable subtract 14 from both sides): 10x = 101

(find the variable divide both sides by 10): x = 101/10

x = 10.1

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.