Sum and Difference of Angles: Using angles in a triangle

ΔABD is a right triangle.

$∢\text{CAD}=\text{?}$

Let's look at triangle ABD and note that we are given two angles: 90 and 17.

Since the sum of angles in a triangle equals 180, we can calculate angle BAD as follows:

$180-90-17=73$

Since we are given angle BAC, we can calculate angle CAD as follows:

$73-61=12$

12

AD bisects $∢BAC$.

Calculate the size of $∢ACB$.

Let's remember that an angle bisector divides the angle into 2 equal parts, therefore:

$BAD=DAC=20$

We should also note that we are given:

$ADB=ADC=90$

Since the sum of angles in a triangle is 180, we can determine the size of angle ACB as follows:

Let's focus on triangle ACD, where we know 2 angles and calculate:

$ACB=180-90-20$

$ACB=70$

70

According to the data in the diagram, calculate a size of angle ABC.

Note from the diagram that we can know the value of angle BAC, since its corresponding angle is equal to 105.

Now in the triangle we are given two angles:

$BAC=105$

$BCA=45$

Since the sum of angles in a triangle is equal to 180, we can calculate angle ABC:

$180-105-45=30$

30

ABC is an isosceles triangle.

$∢A=4x$

$∢B=2x$

Calculate the value of x.

As we know that triangle ABC is isosceles.

$B=C=2X$

It is known that in a triangle the sum of the angles is 180.

Therefore, we can calculate in the following way:

$2X+2X+4X=180$

$4X+4X=180$

$8X=180$

We divide the two sections by 8:

$\frac{8X}{8}=\frac{180}{8}$

$X=22.5$

22.5

According to the data,

Calculate the size $∢\text{BAC}$

Since we are given an angle of 147, let's calculate the angle ACB which complements it to 180 degrees:

$180-147=33$

Now we have two angles in triangle ABC, and we can calculate angle BAC:

$180-90-33=57$

57

Triangle ABC isosceles.

AB = BC

Calculate angle ABC and indicate its type.

Given that it is an isosceles triangle:$AB=BC$

It is possible to argue that:$BAC=ACB=45$

Since the sum of the angles of a triangle is 180, the angle ABC will be equal to:

$180-45-45=90$

Since the angle ABC measures 90 degrees, it is a right triangle.

90°, right angle.

Calculate the value of x.

Remember that a straight angle is equal to 180 degrees.

Let's note that angle 111 and angle ACB together form a straight angle.

Let's calculate angle ACB as follows:

$ACB=180-111$

$ACB=69$

Now we can calculate X.

Remember that the sum of angles in a triangle is equal to 180 degrees, therefore:

$X=180-69-60$

$X=51$

51

ABC is a triangle. What is the size of the angle $∢\text{BAD}$?

First, let's find the value of angle B.

Since the sum of angles in a triangle is equal to 180, the formula is:

$180-86-28=66$

Now let's look at angle ADB, we can calculate its value since we are given angle ADC.

$180-122=58$

Now we can calculate angle BAD:

$180-66-58=56$

56

The angles below are between parallel lines.

What is the value of X?

Our initial objective is to find the angle adjacent to the 94 angle.

Bearing in mind that adjacent angles are equal to 180, we can calculate the following:

$180-94=86$
Let's now observe the triangle.

Considering that the sum of the angles in a triangle is 180, we can determine the following:

$180=x+53+86$

$180=x+139$

$180-139=x$

$x=41$

41°

ΔABC is a right triangle.

$∢\text{ABC}=50$

Calculate the size of angle $∢\text{MAB}$.

Since we are given that AM bisects BC, we can claim that AM is a median, therefore:

$AM=BM=MC$

As a result, we have created an isosceles triangle BMA, where $BM=MA$

Since we are given that angle B is equal to 50, and in an isosceles triangle the base angles are equal to each other, we can claim:

$B=MAB=50$

50

What is the value of X given the angles between parallel lines shown above?

Due to the fact that the lines are parallel, we will begin by drawing a further imaginary parallel line that crosses the 110 angle.

The angle adjacent to the angle 105 is equal to 75 (a straight angle is equal to 180 degrees) This angle is alternate with the angle that was divided using the imaginary line, therefore it is also equal to 75.

In the picture we are shown that the whole angle is equal to 110. Considering that we found only a part of it, we will indicate the second part of the angle as X since it alternates and is equal to the existing X angle.

Therefore we can say that:

$75+x=100$

$x=110-75=35$

35°

Below is the triangle ABC.

The sum of the angles $∢A$ and $∢B$ is twice the size of angle $∢C$.

Calculate $∢C$.

60°

ABC Right triangle

$∢\text{BAC}=30$

Calculate the size $∢\text{CBD}$

30

Shown below is the triangle ABC.

$∢A$ is 3 times greater than the sum of the rest of the angles.

Calculate $∢A$.

135°

The triangle ABC is right angled.

$∢A=4∢B$

Calculate angles $∢B$ and $∢A$.

72 , 18

ABC is a right triangle.

$∢A=20°$

Is it possible to calculate the size of $∢C$?

If so, what is it?

Yes, 70°.

Given the triangle ABC.

Dado ∢B>90° , $∢A=20°$

Is it possible to calculate a ? $∢B$?

If so, find how much the angle is equal to.

$$

No

Calculate the values of x, y, and z.

x = 33, y = 75, z = 50

Calculate the values of x and y.

y=43, x=47

The triangle ABC is isosceles.

$∢C=50°$

Is it possible to calculate the size of angle $∢A$?

If so, then what is it?

Yes, 80°