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Maths-

General

Easy

Question

In Triangle ABC , AB= AC, and D is a point on AB. Such that AD=DC=BC. Show that $straight angle B A C equals 36 to the power of ring operator$

hint Hint:

Use the property of isosceles triangle.

The correct answer is: 36°

In ΔABC, we have
CD = BC (given)
Let $straight angle D B C equals straight angle B D C equals x to the power of ring operator$ (since angles opposite to the equal sides are always equal)
Since AB = AC, $straight angle A B C equals straight angle A C B equals x to the power of ring operator$
In ΔABC,
$straight angle A B C plus straight angle A C B plus straight angle B A C equals 180 to the power of ring operator$ (By angle sum property of the triangle)
$table attributes columnspacing 1em end attributes row cell straight angle B A C plus x plus x equals 180 to the power of ring operator end cell row cell straight angle B A C equals 180 to the power of ring operator minus 2 x end cell end table$
Since AD = CD (given),
$straight angle A C D equals straight angle D A C$
So, $straight angle D A C equals 180 to the power of ring operator minus 2 x$
Now, $straight angle B C D equals straight angle A C B minus straight angle A C D equals x minus open parentheses 180 to the power of ring operator minus 2 x close parentheses equals 3 x minus 180 to the power of ring operator$
$straight angle B D C plus straight angle D B C plus straight angle B C D equals 180 to the power of ring operator$ (angle sum property)
$x plus x plus 3 x minus 180 equals 180 to the power of ring operator$
$table attributes columnspacing 1em end attributes row cell not stretchy rightwards double arrow 5 x equals 360 to the power of ring operator end cell row cell not stretchy rightwards double arrow x equals 72 to the power of ring operator end cell end table$
Now, $straight angle B A C equals 180 minus 2 x equals 180 minus 2 left parenthesis 72 right parenthesis equals 36 to the power of ring operator$ .

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