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Mathematics

Grade-8

Easy

Question

The measure of angles m, n are __ and _.

$∠ m = 45 ° and ∠ n = 45 °$
$∠ m = 60 ° and ∠ n = 60 °$
$∠ m = 35 ° and ∠ n = 45 °$
$∠ m = 60 ° and ∠ n = 60 °$

hint Hint:

In triangle XZT, XZ = ZT
So, $angle T X Z$ = $angle Z T X$
Hence, $angle m space$ = 35
Now, in triangle XZT,
The sum of all the interior angles of a triangles is 180.

The correct answer is: $angle m equals 35 degree text and end text angle n equals 45 degree$

In triangle XZT, XZ = ZT
So, $angle T X Z$ = $angle Z T X$
Hence, $angle m space$ = 35

Now, in triangle XZT,
The sum of all the interior angles of a triangles is 180.
$rightwards double arrow angle X Z T plus 35 degree plus 35 degree equals 180 degree$
$rightwards double arrow angle X Z T equals 180 degree minus 70 degree$
$rightwards double arrow angle X Z T equals 110 degree$
In triangle XYZ, $angle X Z T$ is the exterior angle, and $angle n$ and $angle y x z$ are the remote interior angles.
So, $110 degree equals angle n plus 65 degree angle n equals 110 degree minus 65 degree angle n equals 45 degree$
So, the measure of $angle n$ = 45

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