Solving for Triangle Angle C
The sum of the interior angles in any triangle is always $180^\circ$. This fundamental property can be represented by the formula:
$ \text{Angle A} + \text{Angle B} + \text{Angle C} = 180^\circ $
Applying the Angle Sum Theorem
We are given the measures of two angles:
- Angle A = $30^\circ$
- Angle B = $45^\circ$
Substitute these values into the formula:
$ 30^\circ + 45^\circ + \text{Angle C} = 180^\circ $
Calculating Angle C
First, sum the known angles:
$ 75^\circ + \text{Angle C} = 180^\circ $
Next, isolate Angle C by subtracting $75^\circ$ from both sides:
$ \text{Angle C} = 180^\circ - 75^\circ $
$ \text{Angle C} = 105^\circ $
Therefore, the measure of angle C is $105^\circ$.
Similar Questions
- In $\triangle ABC$, $BD \perp AC$ at $D$ and $\angle DBC = 40^\circ$. $E$ is a point on $BC$ such that $\angle CAE = 37^\circ$. What is the measure of $\angle AEB$?
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- The total measure of angles in a triangle is:
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Important Questions from Triangles
Among the following options, which are NOT sides of a triangle?
In a Δ ABC, if ∠A = 120° and AB = AC, then the values of ∠B and ∠C are respectively:
In the equilateral Δ ABC, the base BC is trisected at D and E. The line through D, Parallel to AB, meets AC at F and the line through E parallel to AC meets AB at G. If EG and DF intersect at H, then what is the ratio of the sum of the area of parallelogram AGHF and the area of the Δ DHE to the area of the Δ ABC?
The product of the perimeter of a triangle, the radius of its in‐circle, and a number gives the area of the triangle. The number is
A man goes 24 m towards east and then 10 m towards north. How far is he away from his initial position?
