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I need help! I don’t know this problem can you figure this out?

I need help! I don’t know this problem can you figure this out?-example-1
User Tristan
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The exterior angle theorem states that the measure of each exterior angle of a triangle is equal to the sum of the opposite and non-adjacent interior angles.

Remember that the two non-adjacent interior angles opposite the exterior angle are sometimes referred to as remote interior angles.

The exterior angle is m < 2a°, while the remote interior angles inside the triangle are m < (a + 10)° and m < 44°.

The following equality statement reflects the exterior angle theorem:

m < (a + 10)° + m < 44° = m < 2a°

At this point, you could solve for the value of "a" algebraically:

a + 10 + 44 = 2a

a + 54 = 2a

Subtract "a" from both sides:
a - a + 54 = 2a - a
54 = a

Now that you have the value for a = 54, substitute this value into the given angles to know their measures:

m < (a + 10)° + m < 44° = m < 2a°

m < [(54) + 10] + m < 44 = m < 2(54)

m < 64° + m< 44° = m < 108°

Therefore:

m < (a + 10)° = 64°
m < 2a° = 108°
User Shaun Scovil
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