Question

Two angles of a quadrilateral measure 155° and 125° respectively. The other two angles equal. Find
the measure of each of these equal angles .​

Answer 1

$\large\underline\bold\red{Given:-}$

Two angles of a quadrilateral measure 155° and 125°. And, the other two angles are equal.

$\large\underline\bold\red{To\:find:-}$

The measure of each of these equal angles.

Let the other angles of the Quadrilateral be x .

$\underline\red{\bf\tt{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

• Sum of all angles of the Quadrilateral is 360°.

Therefore,

$:\implies\sf x + x + 155^{\circ} + 125^\circ = 360^\circ \\\\\\:\implies\sf 2x + 280^\circ = 360^\circ\\\\\\:\implies\sf 2x = 360^\circ - 280^\circ\\\\\\:\implies\sf 2x = 80\\\\\\:\implies\sf x = \cancel\dfrac{80^\circ}{2}\\\\\\:\implies{\underline{\boxed{\tt{\red{x = 40^\circ}}}}}$

$\therefore{\underline\red{\tt{Hence,\; measure\;of\;each\;equal\:angle\;is\; \bf{40^\circ }.}}}$

$\rule{300px}{.4ex}$⠀⠀⠀⠀⠀

Answer 2

Answer:

Given :

Two angles of a quadrilateral = 155° and 125°

The other two angles are equal..

To find :

Measure of each angle

Solution :

In a quadrilateral, there will be 4 angle, we have 2 angle's measure and also we have other angles which are equal, let's name them x.

We know, that sum of all the angles in a quadrilateral is equal to 360°

Then, according to the question :-

155° + 125° + x° + x° = 360°

280° + 2x° = 360°

2x° = 360° - 280°

2x° = 80°

x° = 80°/2

x° = 40°

Hence, the measure of those equal angles or the other two angles is 40°..

Verification :

Sum of all the angles should be equal to 360°.

155° + 125° + x° + x° = 360°

155° + 125° + 40° + 40° = 360°

280° + 80° = 360°

360° = 360°

L.H.S = R.H.S

Step-by-step explanation:

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