1 Answer

Yamin · Answer 1 · 2022-12-05T06:32:11+0000

Given:

$\Delta MAT\cong \Delta MHT$ and
$m\angle 2=82^\circ$ .

To find:

Whether
$m\angle 1=47^\circ$ is possible or not.

Solution:

We have,

$\Delta MAT\cong \Delta MHT$

$\angle AMT\cong \angle HMT$ (CPCTC)

$m\angle 3=m\angle 8$ ...(i)

And,

$m\angle 1=m\angle 8$ ...(ii) (Vertically opposite angles)

From (i) and (ii), we get

$m\angle 1=m\angle 3$ ...(iii)

Now,

$m\angle 1+m\angle 2+m\angle 3=180^\circ$ (Linear pair)

$m\angle 1+82^\circ+m\angle 1=180^\circ$ (Using (iii))

$2m\angle 1=180^\circ-82^\circ$

$2m\angle 1=98^\circ$

Divide both sides by 2.

$m\angle 1=(98^\circ)/(2)$

$m\angle 1=49^\circ$

The measure of angle 1 is 49 degrees so it cannot be equal to 47 degrees.

Therefore, the required answer is "no", the given statement
$m\angle 1=47^\circ$ is not possible.

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