Question

an angle of a parallelogram exceeds its adjacent angle by 40 Degrees.find the measures of the remaining angles​

Answer 1

Answer :

The angles are :

• 70°
• 70°
• 110°
• 110°

Step-by-step explanation :

Given :

An angle of a parallelogram exceeds its adjacent angle by 40°

To Find :

The measures of the remaining angles​.

Solution :

★ Consider the -

One angle as - y + 40

Another angle as - y

We know that :

★ Angle sum property of a parallelogram = 360°

Now,

$\bigstar\;\boxed{\sf y+40+y+40+y+y=360\textdegree}}$

Values in Equation,

⇒ y  + 40 + y + 40 + y + y = 360°

⇒ 4y + 80 = 360°

⇒ 4y = 360 - 80

⇒ y = $\sf \dfrac{280}{4}$

⇒ y = 70

Therefore,

The angles are :

• 70°
• 70°
• 110°
• 110°

$\rule{300}{1.5}$

★ Extra Information :

• Parallelogram is a two-dimensional quadrilateral.
• It has four has four sides that intersect at four points.
• All angles are right, if one angle is right.
• Parallelograms' diagonals  bisect each other.
• It's consecutive angles are supplementary.

There are 3 types of parallelogram :

Rectangle.

Rhombus.

Square.

Answer 2

Answer:

${\pink{\green{\sf{\therefore Angles\:are=70\degree,70\degree,110\degree,110\degree}}}}$

Step-by-step explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

• In the given question information given about a parallelogram whose relation between angles are given.

• We know opposite angles of parallelogram are equal and opposite sides are also equal.

• We have to find all four angles.

$\underline \bold{given : } \\ \implies let \: one \: angle \: of \: parallelogram = x \\ \implies another \: angle = x + 40 \\ \\ \underline \bold{to \: find : } \\ \implies all \: angles \: of \: parallelogram = ?$

• According to given question :

$\bold{lets \: recall \: properties \: of \: parallelogram} \\ \implies opposite \: angles \: are \: equal \\ \implies opposite \: sides \: are \: equal \\ \implies sum \: of \: all \: angles = 2\pi = 360 \degree \\ \\ \bold{according \: to \: these \: properties} \\ \implies x + x + x + 40 + x + 40 = 360 \degree \\ \implies 4x + 80 = 360 \\ \implies 4x = 360 - 80 \\ \implies 4x = 280 \\ \implies x = \frac{280}{4} \\ \bold{\implies x = 70 \degree} \\ \\ \bold{angles \: are : } \\ \bold{ \implies x = 70 \degree }\\ \bold{\implies x = 70 \degree }\\ \bold {\implies x + 40 = 110 \degree }\\ \bold{\implies x + 40 =110 \degree}$