Question

One angle of a triangle measures 126°. the other two angles are congruent. Enter and solve an equation to find the measure x of the congruent angles.

An equation is (blank)= 180

The congruent angles each measure (blank)°

Fill in the blanks.

Answer 1

To find the measure of the congruent angles in a triangle where one angle is 126°, an equation is set up (126° + 2x = 180°) and solved to show that each congruent angle measures 27 degrees.

Step-by-step explanation:

The sum of the angles in a triangle is 180 degrees. Given that one angle measures 126° and the other two angles are congruent, we can set up an equation to find the measure of the congruent angles, x. The equation is:

126° + x + x = 180°

To solve for x, combine like terms and subtract 126° from both sides:

2x = 180° - 126°

2x = 54°

Now, divide both sides by 2 to solve for x:

x = 54° / 2

x = 27°

So the congruent angles each measure 27°.

Answer 2

first we name the angles if the triangle a, b, c respectively. So the first answer is
a + b + c = 180
since we know 1 angle of the triangle (we can call it a) , we can subtract 'a' which is 126 from 180 degrees, which will become the sum of the congruent angles.