Question

Use the diagram below to complete the questions.

Question 1 : Find the value of x.

Question 2: Match the measurements of angles 1 through 6.

Group of answer choices

Angle 1
[ 65 or 115 ]

Angle 2
[ 65 or 115 ]

Angle 3
[ 65 or 115 ]

Angle 4
[ 65 or 115 ]

Angle 5
[ 65 or 115 ]

Angle 6
[ 65 or 115 ]

Answer 1

Answer: 《answer of Question no. 1 》

hope it helps

Answer 2

★ How to do :-

Here, we are given with a diagram in which there are two lines which are parallel to each other. There is a line passing through that parallel lines which is known as transversal line. In that one exterior angle measures 115°. The other angle which is corresponding to that is measuring as (8x-5)°. That is also measuring 115°. We should find the value of 'x' in that equation. Also, for the other angles we should choose the correct measurements of degrees given in the question. In this question the concepts of corresponding, linear pair, adjacent angles are being used.

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➤ Solution :-

Value of 'x' :-

${\tt \leadsto (8x - 5) = {115}^{\circ}}$

${\tt \leadsto 8x = 115 + 5}$

${\tt \leadsto 8x = 120}$

${\tt \leadsto x = \dfrac{120}{8}}$

${\tt \leadsto x = \cancel \dfrac{120}{8} = \boxed{\tt {15}^{ \circ}}}$

Verification :-

${\tt \leadsto (8x - 5) = 115}$

${\tt \leadsto (8 \times 15 - 5) = 115}$

${\tt \leadsto (120 - 5) = 115}$

${\tt \leadsto 115 = 115}$

Hence verified !!

$\:$

Now,

Measurement of ∠1 :-

This angle measures 65° because the linear pair of angles measure 180°. We can find this value by subtracting 180 and 115.

${\tt \leadsto \orange{\boxed{\tt \angle{1} = {65}^{\circ}}}}$

Measurement of ∠2 :-

This angle measures 115° because the vertically opposite angles are always equal.

${\tt \leadsto \orange{\boxed{\tt \angle{2} = {115}^{\circ}}}}$

Measurement of ∠3 :-

This angle measures 65° because the vertically opposite angles are always equal.

${\tt \leadsto \orange{\boxed{\tt \angle{3} = {65}^{\circ}}}}$

Measurement of ∠4 :-

This angle measures 65° because the corresponding angles are always equal.

${\tt \leadsto \orange{\boxed{\tt \angle{4} = {65}^{\circ}}}}$

Measurement of ∠5 :-

This angle measures 115° because the corresponding angles are always equal.

${\tt \leadsto \orange{\boxed{\tt \angle{5} = {115}^{\circ}}}}$

Measurement of ∠6 :-

This angle measures 65° because the vertically opposite angles are always equal.

${\tt \leadsto \orange{\boxed{\tt \angle{6} = {65}^{\circ}}}}$