Question

in the adjoining figure
find
a) x
b)angle B and angle C​

Answer 1

X= 19

angle B= 109

angle C=118

Answer 2

Answer :-

★ The value of the unknown variable x is 19 °

★ The value of the angles B and C are 109 and 118 degrees respectively

Given that -

• The angles in a quadrilateral are 90° , (2x + 5), (7x - 15) and (6x - 5)

To Find -

• The measure of the variable x in the following figure

Analysis -

ㅤㅤㅤHere by the given picture in the question we can observe that the figure is that of a quadrilateral will has four interior angles which are

• 2x + 5 degrees
• 7x - 15 degrees
• 6x - 5 degrees
• A right angle ( 90° )

ㅤㅤWe know that according to the angle sum property which states that the sum of interior angles in any sort of quadrilateral equals to the measure of 360 degrees so , now let's apply the addressed property and find out the required measures of angles and variables in the quadrilateral ABCD

Solution -

Now let's frame an equation which would represent the satisfaction of angle sum property, In simple words let's add up the angles and represent them in the L.H.S side of the equation

ㅤㅤAs we know that their sum will be equal to 360° so, let's put the value "360°" in the R.H.S part of the equation and use transposition method to solve the equation

Framing an equation we get -

$\twoheadrightarrow \sf 90 + 2x + 5 + 7x - 15 + 6x - 5 = 360 \\ \\ \\ \qquad\twoheadrightarrow \sf 90 + 9x - 10 + 6x - 5 = 360 \\ \\ \\ \qquad\twoheadrightarrow \sf 90 + 15x - 10 - 5 = 360 \\ \\ \\ \qquad\twoheadrightarrow \sf 90 + 15x - 15 = 360 \\ \\ \\ \qquad\twoheadrightarrow \sf75 + 15x = 360 \\ \\ \\ \qquad\twoheadrightarrow \sf 15x = 285 \\ \\ \\ \qquad\twoheadrightarrow \sf x = \cancel\dfrac{285}{15} \\ \\ \\ \qquad {\red{\twoheadrightarrow {\underline{\boxed{\frak{ x = 19 }}}}\star}}$

ㅤ Since we have found out the value of the of the unknown variable now let's substitute it's value in the measure of the angles and find them out in numerical terms

Required Measures -

• Variable x = 19°
• Angle B = 6x - 5 = 6(19) - 5 = 109°
• Angle C = 7x - 15 = 7(19) - 15 = 118°

Therefore -

• The variable x measures 19 degrees and the angles B and c measure 109 degrees and 118 degrees respectively

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬