I need to know how to find the measure of angle a.

90°

Step-by-step explanation:

We need expressions for the measures of the three interior angles. Then we add them and set the sum equal to 180. Then we solve for x. Finally, we use the value of x in x + 100 to find the measure of angle A.

Let's first find an expression for each angle.

Angle A: m<A = x + 100

Bottom left angle: The interior angle is vertical to the angle measuring x + 60, so the interior angle also measures x + 60.

Bottom right angle: Let's call the measure of the interior angle y. y and the angle measuring 140° are supplementary, so y + 140 = 180; y = 40.

Now that we have expressions for the three interior angle measures, we add them and set the equal to 180.

(x + 100) + (x + 60) + 40 = 180

x + 100 + x + 60 + 40 = 180

2x + 200 = 180

2x = -20

x = -10

The measure of angle A is x + 100, and x = -10

m<A = x + 100 = -10 + 100 = 90

90°

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