There room many types of triangles in the human being of geometry. Over there is a distinct triangle called an isosceles triangle. In one isosceles triangle, the basic angles have actually the same level measure and also are, together a result, same (congruent). Similarly, if 2 angles of a triangle have actually equal measure, climate the sides the opposite those angles are the very same length. The easiest means to define an isosceles triangle is the it has actually two equal sides.

In one isosceles triangle, we have two sides dubbed the legs and also a third side dubbed the base. The angle located opposite the base is referred to as the vertex.

### Sample A:

The vertex angle B that isosceles triangle alphabet is 120 degrees. Find the level measure of each base angle.

You are watching: Triangle abc is an isosceles right triangle. what is the measure of a base angle? ° Solution:

(1) let x = the measure of every base angle. (2) set up one equation and solve for x. basic angle + basic angle + 120 levels = 180 degrees x + x + 120 levels = 180 levels 2x + 120 = 180 2x = 180 - 120 2x = 60 x = 60/2 x = 30

every base edge of triangle ABC procedures 30 degrees.

### Sample B:

In isosceles triangle RST, angle S is the crest angle. Base angle R and also T both measure 64 degrees. Discover the level measure the the vertex edge S. Solution:

(1) allow x = measure up of vertex angle S. (2) set up an equation and also solve for x.

basic angle + basic angle + vertex edge S = 180 levels 64 levels + 64 degrees + x = 180 degrees 128 + x = 180 x = 180 - 128 x = 52

The measure up of vertex edge S in triangle RST is 52 degrees.

### Sample C:

The degree measure the a base angle the isosceles triangle XYZ exceeds three times the degrees measure the the crest Y by 60. Uncover the degree measure of the vertex angle Y. Notice that it"s hard to attract a picture without learning which angles are largest. We should make an equation out of this problem, therefore let"s number out what it"s trying come tell us. First we review "The level measure of a basic angle", so let"s start with X=

Our equation for this reason far: X=

Now we watch "exceeds 3 times... Y... By 60", which way 3Y + 60.

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Our equation now: X = 3Y + 60

Since we recognize that X = Z because it is an isosceles triangle, then we have the right to solve because that the measures of every the angles.

base angle + basic angle + peak = 180 X + Y + Z = 180 (3Y + 60) + Y+ (3Y + 60) = 180 7Y + 120 = 180 7Y = 60 Y = 60/7 Y = 8.57 degrees