Question

2. 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

Given:

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

To find:

• The measure of each of these equal angles.

❍ Let the other angles of the Quadrilateral be x.

⠀⠀⠀

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

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

Therefore,

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

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

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀⠀

$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: Verification \: :}}}}}\mid}$⠀

• As We know that, Sum of all angles of the Quadrilateral is 360°. And, we're given with measure of two angles. Let's verify:

⠀⠀⠀

$:\implies\sf 40^{\circ} + 40^\circ + 155^\circ + 125^\circ = 360^\circ \\\\\\:\implies\sf 80^\circ + 280^\circ = 360^\circ \\\\\\:\implies\sf 360^\circ = 360^\circ$

⠀⠀⠀

$\qquad\quad\therefore{\underline{\textsf{\textbf{Hence Verified!}}}}$

Answer 2

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

Learn more

Few Properties of quadrilaterals :-

1. Opposite angles are equal and parallel.
2. Diagonals bisect each other.
3. Sum of any two adjacent angles is 180°.
4. Diagonals are equal and are perpendicular bisectors of each other.

Types of quadrilaterals :-

1. Trapezoid
2. Parallelogram
3. Square
4. Rectangle
5. Rhombus
6. Kite

Every 2D figure is a type of quadrilateral.