Question

Answer this now please

Answer 1

Answer:

when x=60 degree then y=60 degree

and when y= 40 degree then x=70 degree

Answer 2

• (a) y = 60° [when x = 60°]
• (b) x = 70° [when y = 40°]

Step-by-step explanation:

In the question, it's been given a figure where, two line segments PQ and MN intersect at a point O. The measures of ∠MOP and ∠MOQ has been given as 2x and y, respectively. We've been asked to:

ㅤㅤ(a) Determine y, when x = 60°

ㅤㅤ(b) Determine x, when y = 40°

By observing the given figure, we can say that it represents vertically opposite angles. So, the measures of its opposite angles are identical, i.e., ∠MOP = ∠NOQ and ∠MOQ = ∠NOP.

(a) Determining the value of y:

ㅤㅤㅤSince ∠MOP and ∠MOQ are linear pairs, their sum equals to 180°. And in the question, it has been given that x equals to 60°. Hence,

$\twoheadrightarrow{ \sf{ \angle MOP + \angle MOQ = 180 \degree}}$

Plugging in the given values.

$\twoheadrightarrow{ \sf{2x+ y = 180}}$

Writing the value of x.

$\twoheadrightarrow{ \sf{2(60) + y = 180}}$

Multiplying the terms.

$\twoheadrightarrow{ \sf{120+ y = 180}}$

Transposing the like terms.

$\twoheadrightarrow{ \sf{180 - 120 = y }}$

Subtracting the terms.

$\twoheadrightarrow{ \sf{60=y }}$

• Therefore, we can say that the value of y, when x equals to 60° is 60°.

(b) Determining the value of x:

⠀⠀⠀⠀⠀As we know that ∠MOP and ∠MOQ are linear pairs, just like how we have solved the first sub-question, we can solve this too. Here, it's been given that y = 40°.

$\twoheadrightarrow{ \sf{ \angle MOP + \angle MOQ = 180 \degree}}$

Plugging in the values.

$\twoheadrightarrow{ \sf{2x+ y = 180}}$

Writing the value of y.

$\twoheadrightarrow{ \sf{2x + 40 = 180}}$

Transposing the like terms.

$\twoheadrightarrow{ \sf{2x = 180 - 40}}$

Subtracting the terms.

$\twoheadrightarrow{ \sf{2x = 140}}$

Again transposing the like terms.

$\twoheadrightarrow{ \sf{x = \dfrac{140}{2} }}$

Reducing the fraction to its lowest form.

$\twoheadrightarrow{ \sf{x = 70}}$

• Therefore, we can say that the value of x, when y equals to 40° is 70°.