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2 years ago

Find the measures of 21 and 22 80° 2102°

Mathematics

1 answer:

cestrela7 [59]2 years ago

4 0

Answer:

Angle 1 is 22°

Angle 2 is 78°

Step-by-step explanation:

Angles on a straight line always add up to 180°.

To find Angle 2, you would have to do 180° take away 102°.

180-102=78°

Angles in a triangle also add up to 180°.

So to find Angle 1, you would have to add the two Angles you already have and take it away from 180°.

80+78=158°

180-158=22°

Hope this helps :)

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Step-by-step explanation:

$\bold{ELIMINATION\ METHOD}\\\\\left\{\begin{array}{ccc}y=-x+8\\y=x+4&\TEXT{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}y=-x+8\\-y=-x-4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad0=-2x+4\qquad\text{add}\ 2x\ \text{to both sides}\\.\qquad2x=4\qquad\text{divide both sides by 2}\\.\qquad\boxed{x=2}\\\\\text{Put it to the second equation}\\y=2+4\\\boxed{y=6}$

$\bold{SUBSTITUTION\ METHOD}\\\\\left\{\begin{array}{ccc}y=-x+8&(1)\\y=x+4&(2)\end{array}\right\\\\\text{Substitute (1) to (2)}\\\\-x+8=x+4\qquad\text{subtract 8 from both sides}\\-x=x-4\qquad\text{subtract}\ x\ \text{from both sides}\\-x-x=-4\\-2x=-4\qquad\text{divide both sides by (-2)}\\\boxed{x=2}\\\\\text{Put it to the second equation}\\y=2+4\\\boxed{y=6}$

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