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Mathematics

Grade-8

Easy

Question

Find the measures of unknown angles in the given figure.

$∠ 1 = 90 ° and ∠ 2 = 90 °$
$∠ 1 = 120 ° and ∠ 2 = 60 °$
$∠ 1 = 90 ° and ∠ 2 = 45 °$
$∠ 1 = 100 ° and ∠ 2 = 55 °$

hint Hint:

We know the measure of the exterior angle is equal to the sum of remote interior angles.

The correct answer is: $angle 1 equals 100 degree text and end text angle 2 equals 55 degree$

In the bigger triangle, 120o is the exterior angle and angle 1 and 20 are remote interior angles.
We know the measure of the exterior angle is equal to the sum of remote interior angles.
So,120=angle 1+20
angle 1=120-20
angle 1=100
Now, for the smaller triangle, angle 1 is the exterior angle
angle 1=angle 2+45
angle 2=100-45
angle 2=55
So, the measure of angle 1 = 100 and angle 2 = 55

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