Question

Please ignore the writing in blue as I tried to work it out but couldn’t

Answer 1

`k=35`°

Explanation:

The degree measure of a straight line is (180) degrees. Therefore, when a line intersects another line, the sum of angle measures on any one side of the line is (180). One can apply this here to find the supplement (the angle on the same side of the line) of the angle with a measure of (130) degrees, and (85) degrees.

`130 + (unknown_1)=180\\unknown_1=50\\\\85+(unknown_2)=180\\unknown_2=95`

The sum of angle measures in a triangle is (180) degrees, one can apply this here by stating the following;

`(unknown_1)+(unknown_2)+(k)=180`

Substitute,

`50+95+k=180`

Simplify,

`50+95+k=180\\\\145+k=180\\\\k=35`

Answer 2

`\sf \bf {\boxed {\mathbb {TO\:FIND :}}}`

The measure of angle
`k`.

`\sf \bf {\boxed {\mathbb {SOLUTION:}}}`

`\implies {\blue {\boxed {\boxed {\purple {\sf {k\:=\:35°}}}}}}`

`\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}`

We know that,

`\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}`

➪
`x` + 85° = 180°

➪
`x` = 180° - 85°

➪
`x` = 95°

Also,

Exterior angle of a triangle is equal to sum of two opposite interior angles.

And so we have,

➪ 130° =
`k` +
`x`

➪
`k` + 95° = 130°

➪
`k` = 130°- 95°

➪
`k` = 35°

Therefore, the value of
`k` is 35°.

`\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}`

`\sf\blue{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}`

➪ 50° + 35° + 95° = 180°

( where 50° = 180° - 130°)

➪ 180° = 180°

➪ L. H. S. = R. H. S.

Hence verified.

(Note: Kindly refer to the attached file.)

`\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}`