Question

PLEASE. HELP. ME.

Find the measure of the missing angles.

Answer 1

• see below

Explanation:

To find:-

• The values of m , k , g and h .

Answer:-

From the given figure we can see that angles k and 121° are vertically opposite angles . Also we know that vertically opposite angles are equal to each other. Hence here we can say that,

`\longrightarrow \boxed{ k = 121^o}\\`

Secondly, we know the the mesure of angle of a straight line is 180° . So the sum of angles on a straight line would be 180° . If two angles are present we call them linear pair . Hence here , we can see that m and 121° are linear pairs.

So that,

`\longrightarrow m + 121^o = 180^o \\`

`\longrightarrow m = 180^o-121^o\\`

`\longrightarrow \boxed{m = 59^o } \\`

Similarly we can see that g and 119° are vertically opposite angles. Again they will be equal. So ,

`\longrightarrow \boxed{g = 119^o} \\`

Again, 119° and h form linear pair.So their sum would be 180° .

`\longrightarrow h + 119^o = 180^o \\`

`\longrightarrow h = 180^o - 119^o\\`

`\longrightarrow \boxed{ h = 61^o }\\`

These are the required values of the unknown angles.

Answer 2

∠h = 61°

∠g = 119°

∠m = 59°

∠k = 121°

Explanation:

According to the Vertical Angles Theorem, when two straight lines intersect, the opposite vertical angles are congruent.

Therefore, as angle g is opposite 119°:

⇒ ∠g = 119°

As angle k is opposite 121°:

⇒ ∠k = 121°

Angles on a straight line sum to 180°.

As angle h and 119° form a straight line:

⇒ ∠h + 119° = 180°

⇒ ∠h + 119° - 119° = 180° - 119°

⇒ ∠h = 61°

As angle m and 121° form a straight line:

⇒ ∠m + 121° = 180°

⇒ ∠m + 121° - 121° = 180° - 121°

⇒ ∠m = 59°