Question

1.5 triangles
score: 1/16 answered: 1/16
question 2
two angles of a triangle have the same measure and the third orlas is 45 degrees greater than the measure of each of the other two. find the measure of the largest angle in the triangle.
answer: the largest angle has a measure of degrees.

Explanation:

Step1: Let the measure of the two equal angles

Let the measure of each of the two equal angles be \(x\) degrees. Then the measure of the third (largest) angle is \((x + 45)\) degrees.

Step2: Use the triangle - angle sum formula

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(x+x+(x + 45)=180\).
Combine like terms: \(3x+45 = 180\).
Subtract 45 from both sides: \(3x=180 - 45\), so \(3x=135\).
Divide both sides by 3: \(x=\frac{135}{3}=45\).

Step3: Find the measure of the largest angle

The measure of the largest angle is \(x + 45\). Substitute \(x = 45\) into \(x + 45\), we get \(45+45=90\).

Answer:

\(90\)