Question

Can you answer this and explain the answer.

Answer 1

Value of x: 10°

m<1 = 53°

m<2 = 53°

Explanation:

Since given,

• r || s,

This signifies we can apply theorem based on parallel lines.

In the figure given adjacent to the question, we can see r and s are parallel and a line(known as transversal) cuts it.

We can apply: Corresponding angle theorem,which says:

• Angles on a parallel, to the transversal, which are corresponding to other angle,are equal.
• In the given figure, <1 = <2 since the angle are correspondent to each other on parallel.

Hence according to the question,

• <1 = <2

Given m<1 = 63-x

m<2 = 73-2x

So,

• m<1 = m<2

So,our equation stands at:

• 73 -2x = 63-x

Solving the equation:

• 73 -63 = 2x-x
• 10 = x
• x = 10.

Putting the value of x to get m<1:

• 63-x = 63 - 10 = 53°

Similarly for m<2:

• 73-2x
• 73-2*10 = 73-20 = 53°

Answer 2

m∠1 = 53

m∠2 = 53

Explanation:

Corresponding angles are angles that are in the same position on two parallel lines that are intersected by a transversal.

Corresponding angles are always congruent, which means that they have the same measure.

In this case:

m∠1 and m∠2 are corresponding angles.

m∠1 = m∠2

Substituting value:

63 - x = 73 - 2x

Add 2x on both sides;

63 - x + 2x = 73 - 2x + 2x

63 + x = 73

Subtract 63 on both sides:

63 + x - 63 = 73 - 63

x = 10

Now

We can find the value of angles by substituting the value of x in the given expression, we get.

m∠1 = 63 - 10

= 53

m∠2 = 73 - 2 × 10

= 73 - 20

= 53

Therefore,

m∠1 = 53

m∠2 = 53