Question

The vertex angle of an isosceles triangle measures 40°. What is the measure of a base angle?

Answer 1

A triangle has three angles, and their measures add up to 180 degrees.
An isosceles triangle has at least 2 congruent sides, and the angles opposite the congruent sides are congruent.

This triangle has one angle of 40 deg, and two angles that measure the same; call the measure of each base angle x.

x + x + 40 = 180

2x + 40 = 180

2x = 140

x = 70

The base angles measure 70 deg.

Answer 2

The measure of base angle is $\boxed{{{70}^ \circ }} if the vertex angle is {40^ \circ }$ .

Further explanation:

Given:

Vertex angle of the isosceles triangle is ${40^ \circ }$ .

Explanation:

The triangle three sided close Figure.

There are three type of triangles.

1. Equilateral triangle

2. Isosceles triangle

3. Scalene triangle

Equilateral triangle has all sides equal and all the angles are equal.

Isosceles triangle has 2 sides equal to each other and the two base angles are equal to each other.

Scalene triangle has all sides unequal and the angles are also not equal to each other.

The sum of all the angles of the triangle is ${180^ \circ }$.

Consider the base angle as y.

The value of y can be obtained as follows,

$\begin{aligned}y+y+40&=180\\2y+40&=180\\2y&=180-40\\2y&=140\\y&=\frac{{140}}{2}\\y&={70^ \circ }\\\end{aligned}$

The measure of base angle is $\boxed{{{70}^ \circ}} if the vertex angle is {40^ \circ}$.

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: vertex angle, isosceles triangle, base angle, perpendicular, altitudes, point, triangle, circumcenter, bisectors, perpendicular bisectors, angles, angle bisectors, median, intersection, incenter, right angle triangle, equilateral triangle, obtuse, acute.