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Mathematics

Grade-8

Easy

Question

If $C D ‖ B A$ , find the measure of angles 1, 2, and 3 and name the triangle based on its angles.

$∠ 3 = 60 ° and ∆ A B C is an equilateral triangle.$
$∠ 3 = 90 ° and ∆ A B C is a right triangle.$
$∠ 3 = 45 ° and ∆ A B C is an isosceles triangle.$
$∠ 3 = 90 ° and ∆ A B C is a right isosceles triangle.$

hint Hint:

We know alternate interior angles are equal.
The sum of all the interior angles of a triangle is 180.

The correct answer is: $angle 3 equals 90 degree text and end text increment A B C text is a right isosceles triangle. end text$

Since $C D ‖ B A comma$ so, $angle 1$ and 45o are the alternate interior angles.
We know alternate interior angles are equal.
So, $angle 1$ = 45o
$text Also, in triangle end text ABC comma AB equals BC$
Since the angles opposite to equal sides are equal, we get $angle 1 equals angle 2$
$text Hence, end text angle 1 equals angle 2 equals 45 degree$
Now, in triangle ABC,
The sum of all the interior angles of a triangle is 180o.
$rightwards double arrow angle 1 plus angle 2 plus angle 3 equals 180 degree$
$rightwards double arrow 45 degree plus 45 degree plus angle 3 equals 180 degree rightwards double arrow angle 3 equals 180 degree minus 90 degree rightwards double arrow angle 3 equals 90 degree$
$text So, the measure of end text angle 3 text is end text 90 degree text , so the triangle end text ABC text is a right isosceles triangle. end text$

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