Question

I need help pleaseeeeee

Answer 1

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.

$m\angle 1=\dfrac{98^\circ}{2}$

$m\angle 1=49^\circ$

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.