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charle [14.2K]
3 years ago
7

Answer and explanation please?​

Mathematics
1 answer:
Vadim26 [7]3 years ago
7 0

Answer:

x = 6

Step-by-step explanation:

Line M and line V are parallel so,

Given angles must be alternate angles and alternate angles has equal measurement

so we write an equation to find the value of x:

19x - 4 = 110 add 4 to both sides

19x = 114 divide both sides by 19

x = 6

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<h3><u>Answer:</u></h3>

\large\boxed{\pink{\sf \leadsto Value \ of \ LM \ is \ 11 \ units . }}

<h3><u>Step-by-step explanation:</u></h3>

A figure is given to us in which we can see two triangles one is ∆ MPL and other is ∆MPN .

<u>Figure</u><u> </u><u>:</u><u>-</u><u> </u>

\setlength{\unitlength}{1 cm}\begin{picture}(12,12)\linethickness{0.25mm}\put(0,0){\line(1,2){2}} \put(0.001,0){\line(1,0){4}}\put(2,0){\vector(0,1){5}}\put(4,0){\line( - 1,2){2}}\put(0,-0.4){$\bf L $}\put(2,-0.4){$\bf P$}\put(4,-0.4){$\bf N $}\put(2.2,4){$\bf M $}\put(2.8, - .4){$\bf 5 $}\put(1, - .4){$\bf 5 $}\put(3.4, 2){$\bf 11 $}\put(2.3,0){\line(0,1){.3}}\put(2.3,.3){\line( - 1,0){.3}}\end{picture}

\underline{\blue{\sf In\: \triangle MPL \ \& \ \triangle MPN :- }}

\qquad \bullet LP = PN = 5 \:\:(given) \\\\\qquad \bullet MP = MP \:\:(Common) \\\\\qquad \bullet \angle MPN = \angle MPL = 90^{\circ} \:\: (given)

Hence by SAS congruence condition ,

\orange{\bf \triangle MPL \cong \triangle MPN }

Hence by cpct ( Corresponding parts of congruent triangles ) we can say that , LM = NM = 11 units .

<h3><u>Hence </u><u>the</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>LM</u><u> </u><u>is</u><u> </u><u>1</u><u>1</u><u> </u><u>units</u><u> </u><u>.</u></h3>
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2 years ago
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