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4 years ago

True or false? Based only on the given information, it is guaranteed that LN MO.

Mathematics

2 answers:

son4ous [18]4 years ago

6 0

That statement is true

MO is dropping just in the middle of LON, splitting into two congruent right triangles , so it is perpendicular

hope this helps

tekilochka [14]4 years ago

6 0

the answer is A . . . . . . . . . . . . apex

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EleoNora [17]

Answer:

$m\angle CAB=102\dfrac{6}{7}^{\circ}\\ \\m\angle ABC=51\dfrac{3}{7}^{\circ}\\ \\m\angle ACB=25\dfrac{5}{7}^{\circ}$

Step-by-step explanation:

AK is angle A bisector, then

$m\angle BAK=m\angle KAC=x^{\circ}$

BL is angle B bisector, then

$m\angle ABL=m\angle CBL=y^{\circ}$

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$m\angle BAL+m\angle ALB+m\angle LBA=180^{\circ}\\ \\2x+2y+y=180\\ \\2x+3y=180$

Consider triangle ABK. In this triangle,

$m\angle AKB=180^{\circ}-2x^{\circ} \ [\text{Supplementary angles}]$

The sum of the measures of all interior angles in this triangle is $180^{\circ},$ then

$m\angle BAK+m\angle AKB+m\angle KBA=180^{\circ}\\ \\x+(180-2x)+2y=180\\ \\2y-x=0$

Hence,

$x=2y\\ \\2(2y)+3y=180\\ \\4y+3y=180\\ \\7y=180\\ \\y=\dfrac{180}{7}=25\dfrac{5}{7}\\ \\x=\dfrac{360}{7}=51\dfrac{3}{7}$

Find the measures of the triangle ABC:

$m\angle CAB=2x^{\circ}=102\dfrac{6}{7}^{\circ}\\ \\m\angle ABC=2y^{\circ}=51\dfrac{3}{7}^{\circ}\\ \\m\angle ACB=180^{\circ}-102\dfrac{6}{7}^{\circ}-51\dfrac{3}{7}^{\circ}=25\dfrac{5}{7}^{\circ}$

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4 years ago

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3 years ago