** sum of inner Angles in a Triangle ** allisonbrookephotography.com Topical rundown | Geometry overview | MathBits" Teacher sources **Terms the Use call Person:** Donna Roberts

The amount of the actions of the interior angles of a triangle equals 180º. You are watching: What is the measure of angle bcd? m∠bcd = degrees |

1. |

*Solution: m*∠*A + m*∠*B + m*∠*C* = 180 38 + *x *+ (*x* + 2) = 180 40 + 2*x* = 180 2*x* = 140 *x *= 70 = *m∠B* *x *+ 2 = 72 = *m∠C*

2. The angle in a triangle are represented by (4

*x*- 6)º, (2

*x*+ 1)º and (

*x*+ 3)º. Is this a ideal triangle?

*Solution:* ** (4 x - 6) + (2x + 1) + (x + 3) = 180 7x - 2 = 180 7x = 182 x = 26 (4x - 6)º = 98º (2x + 1)º = 53º (x + 3)º = 29º No. The triangle is obtuse.**

**3.**

*Solution:* *m*∠*BCD* = 56º. In Δ*ABC,* 85º + 56º + *m*∠*BCA* = 180 *m*∠*BCA* = 39º *m*∠*ACD* = 56º - 39º = 17º

4. The angles in a triangle are in the ratio of 1 : 2 : 3. Discover the measure up of the angle in the triangle.

See more: What Does Fambam Mean Ing And Definition, Fambam Meaning And Definition

*Solution: *** x + 2x + 3x = 180 6x = 180 x = 30 The angles room 30º, 60º, and 90º. **

In her previous studies of this theorem, girlfriend most likely saw how a triangle"s angles deserve to be cut off and rearranged to kind a directly angle the 180º (as displayed below).

We now have to use much more sophisticated principles to develop that this organize is actually true. Throughout history, several different methods of evidence of this theorem have appeared. Let"s take a look at a couple of of these methods of proof.