Question

Find the value of [x].

Answer 1

x = 80°

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°.

The triangle shown in the image is an isosceles triangle, and in isosceles triangles, base angles are congruent.

Then, the measure of x can be calculated as follows:

50 + 50 + x = 180

• Add like terms.

100 + x = 180

• Subtract 100 from both sides.

x = 80

Answer 2

The closest possible integer value for x considering a valid triangle would be x=129

If ∠A=50 and ∠B=x in triangle ABC, we can find the value of x using the fact that the sum of angles in a triangle is 180 :

∠C=180 −∠A−∠B

Given

∠A=50 , let's substitute that into the equation:

∠C=180 −50 −x

∠C=130 −x

Since the sum of angles in a triangle is 180 , we can set up an equation:

∠A+∠B+∠C=180

50 +x +(130 −x )=180

Solving this equation:

50 +130 −x =180

180 −x =180

−x =0

x =0

So, ∠B=x=0

However, this result might be incorrect considering the triangle's properties. Typically, angles in a triangle are greater than 0 degrees, but here it seems to be a special case where the given angle

∠A=50 is probably too large for a valid triangle.

The nearest allowable value for x would be:

If ∠A=50 and ∠B=x , the third angle (∠C) would be:

∠C=180 −∠A−∠B=180 −50 −x =130 −x

For a valid triangle, all angles must be greater than 0. Hence, x should be such that ∠C>0:

130 −x >0

x <130

So, the closest possible integer value for x considering a valid triangle would be x=129