Question

1 - 12. find x and all the missing angles of each triangle
1.
2.
3.
4.

Explanation:

Step1: Use the triangle - angle sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\).

For problem 1:

Step1: Calculate \(x\)

We know that \(x + 50+45=180\).
So \(x=180-(50 + 45)\).

Step2: Simplify the expression

\(x=180 - 95\).
\(x = 85^{\circ}\).
The angles of the triangle are \(\angle A = 50^{\circ}\), \(\angle B=45^{\circ}\), \(\angle C = 85^{\circ}\).

For problem 2:

Step1: Calculate \(x\)

We know that \(x+34 + 41=180\).
So \(x=180-(34 + 41)\).

Step2: Simplify the expression

\(x=180-75\).
\(x = 105^{\circ}\).
The angles of the triangle are \(\angle A = 34^{\circ}\), \(\angle B = 41^{\circ}\), \(\angle C=105^{\circ}\).

For problem 3:

Step1: Calculate \(x\)

We know that \(x + 53+90=180\).
So \(x=180-(53 + 90)\).

Step2: Simplify the expression

\(x=180 - 143\).
\(x=37^{\circ}\).
The angles of the triangle are \(\angle A = 53^{\circ}\), \(\angle B = 37^{\circ}\), \(\angle C = 90^{\circ}\).

For problem 4:

Step1: Calculate \(x\)

We know that \(x+30 + 90=180\).
So \(x=180-(30 + 90)\).

Step2: Simplify the expression

\(x=180-120\).
\(x = 60^{\circ}\).
The angles of the triangle are \(\angle A=30^{\circ}\), \(\angle B = 60^{\circ}\), \(\angle C = 90^{\circ}\).

Answer:

1. \(x = 85^{\circ}\), angles: \(50^{\circ}\), \(45^{\circ}\), \(85^{\circ}\)
2. \(x = 105^{\circ}\), angles: \(34^{\circ}\), \(41^{\circ}\), \(105^{\circ}\)
3. \(x = 37^{\circ}\), angles: \(53^{\circ}\), \(37^{\circ}\), \(90^{\circ}\)
4. \(x = 60^{\circ}\), angles: \(30^{\circ}\), \(60^{\circ}\), \(90^{\circ}\)