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Math  /  Geometry

Question12. Let a equal the measure of angle AA. The equation 360∘=a+90∘+135∘+75∘360^{\circ}=a+90^{\circ}+135^{\circ}+75^{\circ} represents the sum of the angles in the quadrilateral. Find the missing angle measure by solving the equation.

Studdy Solution

STEP 1

1. The sum of the interior angles of a quadrilateral is 360∘ 360^\circ .
2. We need to find the measure of angle A A .

STEP 2

1. Set up the equation.
2. Solve for the missing angle a a .

STEP 3

Write down the equation given in the problem:
360∘=a+90∘+135∘+75∘ 360^\circ = a + 90^\circ + 135^\circ + 75^\circ

STEP 4

Combine the known angle measures on the right side of the equation:
90∘+135∘+75∘=300∘ 90^\circ + 135^\circ + 75^\circ = 300^\circ

STEP 5

Substitute the sum back into the equation:
360∘=a+300∘ 360^\circ = a + 300^\circ

STEP 6

To isolate a a , subtract 300∘ 300^\circ from both sides of the equation:
360∘−300∘=a 360^\circ - 300^\circ = a

STEP 7

Calculate the result:
60∘=a 60^\circ = a
The measure of angle A A is:
60∘ \boxed{60^\circ}

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