Question

Find the value of x and y. Do the sum step by step. I will mark the brainliest answer. If you give wrong answer I will report the answer.​

Answer 1

$\sf\red{AnswEr:-}$

• x° = 64°
• y° = 58°

★GivEn :-

• In given fig. the two angles (except x) of the triangle are equal.
• The adjacent angle of x = 116°

★To FinD :-

• The value of x and y

★ SoluTiOn:-

➬The adjacent angle of x is 116°

➬We know, a straight line contains the angle of 180°

➬So the value of x = (180° - 116°) = 64°

➬ The sum of three angles of a triangle is 180°

➬ The two angles (except x) are equal.

➬ So the sum of those two angles is

$y + y = (180 - 64) \\ \\ = > 2y = 116$

➬ So, the value of y,

$y = \frac{116}{2} = 58$

➬ Therefore, the value of x and y are 64° and 58° respectively.

★VerificatiOn :-

➬ The sum of three angles is 64° + 58° + 58° = 180°

➬ Hence, it is verified.

Answer 2

$\blue\bigstar$Answer:

• x = 64°
• y = 58°

$\pink\bigstar$ Given:

• $\angle$CAB = y
• $\angle$ABC = y
• $\angle$ACB = x
• $\angle$ACD = 116°

$\green\bigstar$To find:

• The value of x and y.

$\red\bigstar$ Solution:

In line BCD,

$\because$ $\angle$ACB and $\angle$ACD are forming Linear Pair,

$\therefore$ $\angle$ACB + $\angle$ACD = 180°

( Linear Pair )

$\implies$ x + 116° = 180°

( $\because$ $\angle$ACB = x and $\angle$ ACD = 116°)

$\implies$ x = 180° - 116°

$\implies$ $\sf\boxed{x\: =\: {64}^{\circ}}$

$\therefore$$\bf\boxed{x\: =\: {64}^{\circ}}$

$\because$ $\angle$CAB + $\angle$ABC = $\angle$ACD

( By exterior Property Of A Triangle)

$\implies$ y + y = 116°

( $\because$ $\angle$CAB = y, $\angle$ ABC = y and $\angle$ACD = 116° )

$\implies$ 2y = 116°

$\implies$ y = $\dfrac{{116}^{\circ}}{2}$

$\implies$ $\boxed{y \:=\: {58}^{\circ}}$

$\therefore$ x = 64° and y = 58°

$\green\bigstar$ Verification:

$\because$ we know that the sum of all angles in a triangle is 180°,

$\therefore$ x + y + y = 180°

(Angle Sum Property Of A Triangle)

$\implies$ 64° + 58° + 58° = 180°

( By substituting the Values)

$\implies$ LHS = RHS

$\therefore$ Verified.

$\blue\bigstar$ Concepts Used:

• Linear Pair
• Exterior Angle Property Of A Triangle

$\pink\bigstar$Extra - Information:

• In a linear pair, the sum of the adjacent angles is 180° and thus they are supplementary.
• A linear pair has supplementary angles, but supplementary angles need not to be a linear pair.
• An exterior angle of a triangle is equal to the sum of the opposite interior angles.