Question

PLZ HELP ME WITH THESE 2 PROBLEMS.

Answer 1

Question 3)

Given -

• Two angle of rhombus = 116°

To find :

Unknown angle

Property used :

• Sum of interior angle of rhombus = 360°
• Opposite angle of rhombus are equal

Solution :

As we are given that two angle are 116° each.

The unknown angle will also equal to each other.

Let - Unknown angle = x

Therefore sum of interior angle of rhombus = 360

➝ 116 + 116 + x + x = 360

➝ 232 + 2x = 360

➝2x = 360 - 232

➝ 2x = 128

➝ x = 128/2

➝ x = 64°

So rest two angle are 64° each

ANSWER : 64° , 64°

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Question 4)

Given :

• Figure us quadrilateral.
• Three angles are given as , 105° , 125° and 75°

To find : x

Property used :

• Sum of interior angle of quadrilateral = 360°

Solution :

Sum of angle = 360°

➝ 105 + 125 + 75 + x = 360

➝ 305 + x = 360

➝ x = 360 - 305

➝ x = 55°

ANSWER : x = 55°

Answer 2

Step-by-step explanation:

Question 3).

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Given: Two of the angles in a rhombus measures 116°.

Need to find: Measures of two unknown angles.

❒ As we know that sum of interior angles of a rhombus is 360° and the opposite angles of a rhombus are equal. So, let the unknown angle be x.

__________________

$\frak{\underline{\underline{\dag According\ to\ the\ question:-}}} \\ \\ \\ \sf : \implies {116\ +\ 116\ +\ x\ +\ x\ =\ 360} \\ \\ \\ \sf : \implies {232\ +\ 2x\ =\ 360} \\ \\ \\ \sf : \implies {2x\ =\ 360\ -\ 232} \\ \\ \\ \sf : \implies {2x\ =\ 128} \\ \\ \\ \sf : \implies {x\ =\ \cancel \dfrac{128}{2}} \\ \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf x\ =\ 64^{\circ}}}}}\bigstar$

$\sf \therefore {\underline{Hence,\ the\ two\ required\ angles\ are\ \bf 64^{\circ}\ \sf each.}}$

Question 4).

__________________

Given: The figure is in the form of a quadrilateral. And three angles are given as 105°, 125°, and 75°.

Need to find: Value of angle x.

❒ As we know that sum of interior angle of a quadrilateral is 360°.

__________________

$\frak{\underline{\underline{\dag According\ to\ the\ question:-}}} \\ \\ \\ \sf : \implies {105\ +\ 125\ +\ 75\ +\ x\ =\ 360} \\ \\ \\ \sf : \implies {305\ +\ x\ =\ 360} \\ \\ \\ \sf : \implies {x\ =\ 360\ -\ 305} \\ \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf x\ =\ 55^{\circ}}}}}\bigstar$

$\sf \therefore {\underline{Hence,\ the\ value\ of\ x\ is\ \bf 55^{\circ}.}}$