How to Find the Measure of an Angle in a Triangle?

Understanding Angle Measurement in a Triangle

In geometry, triangles are one of the fundamental shapes studied. They consist of three sides and three angles. One of the key properties of triangles is that the sum of the angles inside a triangle is always equal to 180 degrees.

Finding the Measure of Angle mcd

The given information tells us that the angle mbc is 105°. We are asked to find the measure of angle mcd. To do this, we can use the fact that the sum of angles in a triangle is 180°.

In triangle MBC, we know that the angle mbc is 105°. Since mbc and mcd are adjacent angles, we can say that the sum of mbc and mcd is equal to the sum of the other two angles in triangle MBC.

Let's denote the other two angles in triangle MBC as angle b and angle c. Therefore, we can form the equation: mbc + mcd = b + c

Substituting the known value of mbc as 105°, the equation becomes: 105° + mcd = b + c

Using the fact that the sum of angles in a triangle is 180°, we rewrite the equation as: 105° + mcd = 180°

To find the measure of mcd, we subtract 105° from both sides of the equation: mcd = 180° - 105°

Simplifying the expression, we get: mcd = 75°

Therefore, the measure of angle mcd is indeed 75°.