Question

Find the fourth angle of a quadrilateral whose three angles are 50°. 110 and
85° respectively​

Answer 1

Answer:

The fourth angle is 115°.

Step-by-step explanation:

• First angle = 50°
• Second angle = 110°
• Third angle = 85°
• Fourth angle = ??

Let,

The Fourth angle of a quadrilateral = x

Following the angle sum property of quadrilateral, all angles sum up to 360°

$\sf{\rightarrow} \: 50^{\circ} + 110^{\circ} + 85^{\circ} + x = 360^{\circ}$

$\sf{\rightarrow} \: 160^{\circ} + 85^{\circ} + x = 360^{\circ}$

$\sf{\rightarrow} \: 245^{\circ} + x = 360^{\circ}$

$\sf{\rightarrow} \: x = 360^{\circ} - 245^{\circ}$

$\sf{\rightarrow} \: x = 115 ^{\circ}$

Fourth angle = 115°

Therefore, the fourth angle is 115°.

Answer 2

${\large{\pmb{\sf{\underline{\maltese \: \: Understanding \; the \; Question...}}}}}$

★ This question says that we have to find the fourth angle of a quadrilateral whose three angles are 50°, 110° and 85° respectively. Hope it's cleared to you all that it's a quadrilateral's angles given and we have to find the fourth one by using a special property. Let's do this question!

${\large{\pmb{\sf{\underline{\maltese \: \: Given \; that...}}}}}$

★ First angle of quadrilateral = 50°

★ Second angle of quadrilateral = 110°

★ Third angle of quadrilateral = 85°

${\large{\pmb{\sf{\underline{\maltese \: \: To \; find...}}}}}$

★ Fourth angle of quadrilateral.

${\large{\pmb{\sf{\underline{\maltese \: \: Solution...}}}}}$

★ Fourth angle of quadrilateral = 115°

${\large{\pmb{\sf{\underline{\maltese \: \: Using \; property...}}}}}$

★ The sum of all the interior angles of a quadrilateral is always 360°

${\large{\pmb{\sf{\underline{\maltese \: \: Full \; Solution...}}}}}$

${\sf{:\implies a \: + b \: + c \: + d \: = 360 \degree}}$

${\sf{:\implies (50+110+85+d) \degree \: = 360 \degree}}$

${\sf{:\implies (160+85+d) \degree \: = 360 \degree}}$

${\sf{:\implies (245+d) \degree \: = 360 \degree}}$

${\sf{:\implies d \degree \: = (360-245) \degree}}$

${\sf{:\implies d \degree \: = 115 \degree}}$

${\sf{:\implies Fourth \: angle \: = 115 \degree}}$

• Henceforth, 115° is the fourth angle of this quadrilateral whose three angles are 50°, 110° and 85°