Question

Please find the unknown angles

Answer 1

Given : the measures of angles in the quadrilateral are 80°, 75°,105° and x

ㅤㅤㅤTo Find : the measure of angle x

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀

❍ here, the measures of the other angles in the quadrilateral are 80°, 75°,105°

ㅤㅤㅤ⠀⠀ㅤㅤㅤ$\maltese \;{\bf{As\; we \; know\; that ,}}$

$\;\;\;\;\;\;\;\bigg[\dag \;\;\bf Sum \; of \; interior \; angles_{(in\; a \; quadrilateral)} = 360 degrees \bigg]$

➛ Now,

• let's frame an equation adding up the angles and state that they are equal to 360°, later transpose the numerical terms and find the value of the variable 'x'

${\underline{\bf{\bigstar{Framing \; an \; equation\; we \;get: }}}}$

${:\implies}\sf 80\degree + 75\degree + 105\degree + x = 360\degree\\ \\ \\{:\implies}\sf 155\degree + 105 \degree + x = 360\degree \\ \\ \\ {:\implies}\sf 260 \degree + x = 360\degree\\ \\ \\ {:\implies}\sf x = 360\degree - 260 \degree\\ \\ \\ {:\implies}\sf {\pink{\underline{\boxed{\pmb{\frak{x = 100\degree}}}}\star}}$

Therefore,

ㅤㅤ⠀ㅤㅤ⠀ㅤㅤ${\underline{\rm{\therefore The \; measure \; of \; the \; unknown \; anglee \; is \;100\degree}}}$

ㅤㅤ⠀

Answer 2

★ The measure of x is 100°.

Step-by-step explanation

Analysis -

‎ ‎ ‎ ‎ ‎ ‎The measure of three angles of a quadrilateral KITE has been given. ∠K = 80°, ∠I = 75°, ∠T = x° and ∠E = 105°. We have been asked to find the measure of ∠T, which is the unknown angle. $\:$

Solution -

‎ ‎ ‎ ‎ ‎ ‎Since the question is about quadrilaterals, let us know about them!

They are simple plane figures bounded by four line segments. Squares, rectangles, trapeziums, rhombi, parallelograms are quadrilaterals.

Consider EFGH as a quadrilateral.

• It has four edges - (EF, FG, GH, EH)
• It has four vertices - (E, F, G, H)
• It has four angles - (∠E, ∠F, ∠G, ∠H) whose sum is 360°.

The above listed properties are the three common properties of any quadrilateral.

Here, we will be using the angle sum property. This property can be simply defined as, “The sum of all the angles i.e, the sum of four angles of a quadrilateral equals 360°”.

According to our question

‎ ‎ ‎ ‎ ‎ ‎ ⇢ ∠K + ∠I + ∠T + ∠E = 360°

‎ ‎ ‎ ‎ ‎ ‎ ⇢ 80° + 75° + x° + 105° = 360°

On simplifying the equation, we get

‎ ‎ ‎ ‎ ‎ ‎ ⇢ 155° + x° + 105° = 360°

‎ ‎ ‎ ‎ ‎ ‎ ⇢ 260° + x° = 360°

Now solving the equation formed

‎ ‎ ‎ ‎ ‎ ‎ ⇢ 260° + x° = 360°

‎ ‎ ‎ ‎ ‎ ‎ ⇢ x° = 360° - 260°

‎ ‎ ‎ ‎ ‎ ‎ ⇢ x° = 100°

Hence

The value of ∠T is 100°

Verification -

Plugging in the obtained value of x in the equation.

‎ ‎ ‎ ‎ ‎ ‎ ⇛ ∠K + ∠I + ∠T + ∠E = 360°

‎ ‎ ‎ ‎ ‎ ‎ ⇛ 80° + 75° + 100° + 105° = 360°

‎ ‎ ‎ ‎ ‎ ‎ ⇛ 155° + 100° + 105° = 360°

‎ ‎ ‎ ‎ ‎ ‎ ⇛ 255° + 105° = 360°

‎ ‎ ‎ ‎ ‎ ‎ ⇛ 360° = 360°

L.H.S. is equal to R.H.S. Therefore, our answer is correct!

___________________________________________________