Question

two angles of quadrilateral measure 74 degree and 166 degree the other two angles are in the ratio 3:5 find the third and The Fourth angles​

Answer 1

Answer:

• Third and fourth angle of quadrilateral will be 45° and 75°

Step-by-step explanation:

Given,

• two angles of quadrilateral are 74° and 166°
• other two angles are in the ratio 3 : 5

We need to find,

• Third and fourth angle

So,

Let, third and fourth angle of quadrilateral be 3 x and 5 x

then,

By angle sum property of quadrilateral , sum of all angles of quadrilateral will be 360°

→ 74° + 166° + 3 x + 5 x = 360°

→ 240° + 8 x = 360°

→ 8 x = 360° - 240°

→ 8 x = 120°

→ x = 120° / 8

→ x = 15°

therefore,

third and fourth angle of quadrilateral will be

• 3 x = 3 (15°) = 45°   and
• 5 x = 5 (15°) = 75° .

Answer 2

Attachment :- Fig of the question

$\mathtt{\huge{\underline{\red{Question\:?}}}}$

✴ Two angles of quadrilateral measure 74 degree and 166 degree the other two angles are in the ratio 3:5 . Find the third and The Fourth angles.

$\mathtt{\huge{\underline{\green{Answer:-}}}}$

✒ The third angle is 45° and fourth angle 75°.

$\mathtt{\huge{\underline{\purple{Solution:-}}}}$

Given :-

• Two angles of quadrilateral measure 74° and 166°.

• The other two angles are in the ratio 3:5.

To Find :-

• The third and fourth angles.

Concept Used :-

Quadrilateral :- A quadrilateral is a four sides plane figure.

Example :- rectangle, square, kite , etc.

• The angle sum property of a quadrilateral is 360°.

Calculation :-

We know that, the sum of the angles of a quadrilateral is 360°.

According to the question,

• Let the unknown sides be x .

• The other two angles are in the ratio 3:5.

So, The other two angles are in the ratio 3x & 5x.

And, given two angles of quadrilateral measure 74° and 166°.

So, by the angle sum property of triangles.

➠ 3x + 5x + 74° + 166° = 360°

➠ 8x + 240° = 360°

➠ 8x = 360 - 240

➠ 8x = 120

➠ x = $\dfrac{120}{8}$

➠ x = $\cancel{\dfrac{120}{8}}$

➠ x = 15

Putting value of x,

➙ 3x = 3 × 15 = 45

➙ 5x = 5 × 15 = 75

➩ The third and fourth angles are 45 & 75.

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$\mathtt{\huge{\underline{\blue{Verification:-}}}}$

The angle sum property of triangles.

3x + 5x + 74° + 166° = 360°

➡ 45° + 75° + 74° + 166° = 360°

➡ 194° + 166° = 360•

➡ 360° = 360°

Here, L.H.S. = R.H.S. So, it gets verified .✔

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