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Triangle ABC is an isosceles right triangle. What is the measure of one base angle? 30º 45º 60º 90º

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HarleyQuinnSwim666

Answer: B: 45º

Step-by-step explanation:

A triangle is a plane figure that has 3 sides and also 3 angles.

The sum of all of the angles of triangle always 180°.

There are several types of triangles such as :

Equilateral Triangle → 3 equal sides

Isosceles Triangle → 2 equal sides

Scalene Triangle → no equal sides

If triangle ABC is an isosceles right triangle , then one of the angles will be 90°. The other two angles ( base angles ) will have the same value.

We could draw this triangle as shown in the attachment.

Let: the base angle = x

x + x + 90º = 180º

2x + 90º = 180º

2x =  180º +  90º

x =  90º ÷ 2  (90 ÷ 2)

x = 45º

The second option is correct because the measure of one base angle is [tex]45^\circ[/tex].

Given:

The triangle ABC is an isosceles right triangle.

To find:

The measure of one base angle of the triangle ABC.

Explanation:

In an isosceles right triangle, one angle is a right angle and the other two angles are base angles with equal measures.

Let [tex]x[/tex] be the measure of one base angle of the triangle. Then the measures of angles of the triangle ABC are, [tex]x,x,90^\circ[/tex].

In triangle ABC,

[tex]x+x+90^\circ=180^\circ[/tex]                (Angle sum property)

[tex]2x=180^\circ-90^\circ[/tex]

[tex]2x=90^\circ[/tex]

Divide both sides by 2.

[tex]x=45^\circ[/tex]

The measure of one base angle is [tex]45^\circ[/tex]. Therefore, the second option is correct.

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