Question

Pl.z hel..p m.e Si r
mat.h geom.etry ques.tion....​

Answer 1

`\\ \rm\Rrightarrow 7x+10+3x+10=180`

`\\ \rm\Rrightarrow 10x+20=180`

`\\ \rm\Rrightarrow 10x=160`

`\\ \rm\Rrightarrow x=16`

Now

• z=7x+10=7(16)+10=112+10=122°
• y=3x+10=3(16)+10=48+10=58°

Answer 2

y = 58°

z = 122°

Explanation:

Linear pair: a pair of adjacent angles formed when two lines intersect. The two angles are always supplementary and so their measures sum to 180°.

Therefore,

(7x + 10) + y = 180

(3x + 10) + z = 180

Alternate interior angle theorem: when 2 parallel lines (AB and CD) are cut by a transversal (EF), the resulting alternate interior angles are equal.

Therefore,

y = (3x + 10)

z = (7x + 10)

Substituting y = (3x + 10) into (7x + 10) + y = 180 and solving for x:

⇒ (7x + 10) + (3x + 10) = 180

⇒ 10x + 20 = 180

⇒ 10x = 160

⇒ x = 16

Calculate angle y and angle z by substituting the found value for x into their equations:

y = 3(16) + 10 = 58°

z = 7(16) + 10 = 122°