Question

The sum of two angles of quadrilateral is 145°.The other two angles are in ratio 2:3. find the angles.​

Answer 1

Answer:

Step-by-step explanation:

Let ABCD be a Quadrilateral.

Where,

AB , AC , BC and CD are the sides of the Quadrilateral.

Angle ACD , Angle ABD , Angle BDC and Angle CAB are the four angles of the Quadrilateral.

The sum of two angle of the Quadrilateral is 145 [ GIVEN ]

Let,

Angle CAB + Angle ABD = 145

And,

Angle BDC : Angle ACD = 2:3

Let , Angle BDC = 2X and Angle ACD = 3X.

We know that the sum of four angles of Quadrilateral is 360°.

So,

Angle CAB + Angle ABD + Angle BDC + Angle ACD = 360°

145 + 2X + 3X = 360. [ CAB + ABD = 145 ]

145 + 5X = 360

5X = 360 - 145

5X = 215

X = 215/5

X = 43°

Therefore,

Angle BDC = 2X =2 × 43° = 86°

Angle ACD = 3X = 3 × 43° = 129°.

Hope it helps :)

Answer 2

Given:

• Sum of two angles in a quadrilateral is 145°.

• Other two sides are in rhe ratio of 2:3.

To find:

• The angles

Solution:

• Let the unknown angle be x

$\tt145 \degree + 2x + </strong><strong>3</strong><strong>x = 360</strong><strong>[</strong><strong>interior \: angl e\:of \: quadrilateral </strong><strong>]</strong><strong>$

$\tt145 \degree + 5x = 360$

$\tt5x = 360 \degree - 145 \degree$

$\tt5x = 215$

$\tt \: x = \dfrac{215}{5}$

$\tt \: x = 43 \degr</strong><strong>e</strong><strong>e$

_________________

As we found the value of (x) is (2)

now,

We can substute the value of x .

2x = 2 * 43

=>86°

3x = 3 * 43

=>129°