<1 &<2 are a linear pair. m<1=x-30 & m<2=x=76. Find the measure of each angle.

Wouldn't it be

x-30+x+76=180

2x+46=180

2x=134

x=67

thus

67-30=37

and

67+76=143

Thanks Steve!!!!!!

thanks

linear pairs add to 180, so (assuming the usual typos)

x-30 + x+76 = 180
x = 77

Now you can figure the two angles.

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To find the measure of each angle, we first need to understand what a linear pair is. A linear pair consists of two adjacent angles that form a straight line, which means their measures add up to 180 degrees.

From the given information, we know that angle <1 and angle <2 form a linear pair. Let's denote the measure of angle <1 as x-30, and the measure of angle <2 as x+76.

Now, we can set up an equation to find the value of x. Since the sum of the measures of angles <1 and <2 is equal to 180 degrees, we have:

(x-30) + (x+76) = 180

Simplifying, we have:
2x + 46 = 180

Next, we isolate the variable x by subtracting 46 from both sides of the equation:
2x = 180 - 46
2x = 134

Finally, we solve for x by dividing both sides of the equation by 2:
x = 134 / 2
x = 67

Great! Now that we have found the value of x, we can substitute it back into the expressions for the angle measures:

Angle <1 = x - 30 = 67 - 30 = 37 degrees
Angle <2 = x + 76 = 67 + 76 = 143 degrees

Therefore, the measure of angle <1 is 37 degrees and the measure of angle <2 is 143 degrees.

Good catch.