Sum and Difference of Angles: Applying the formula

Is it possible...?Isosceles triangle Using variables Calculate Angles in Quadrilaterals Identifying and defining elements Using quadrilaterals Angle bisector Generate a random angle Identify the greater value Using angles in a triangle Finding the size of angles in a triangle

Question 1

Triangle ADE is similar to isosceles triangle ABC.

Angle A is equal to 50°.

Calculate angle D.

Question 2

Triangle ADE is similar to triangle ABC.

Triangle ABC is isosceles.

Angle A is equal to 30°.

Calculate the size of angle E.

Question 3

Triangle ADE is similar to triangle ABC.

Triangle ABC is isosceles.
Angle A is equal to 40°.

Calculate angle D.

Question 4

Triangle ADE is similar to isosceles triangle ABC.

Angle A is equal to 60°.

Calculate angle E.

Question 5

Triangle ADE is similar to equilateral triangle ABC.

Angle A is equal to 20°.

Calculate angle D.

Examples with solutions for Sum and Difference of Angles: Applying the formula

Exercise #1

Triangle ADE is similar to isosceles triangle ABC.

Angle A is equal to 50°.

Calculate angle D.

Video Solution

Step-by-Step Solution

Triangle ABC is isosceles, therefore angle B is equal to angle C. We can calculate them since the sum of the angles of a triangle is 180:

$180-50=130$

$130:2=65$

As the triangles are similar, DE is parallel to BC

Angles B and D are corresponding and, therefore, are equal.

B=D=65

Answer

$65$ °

Exercise #2

Triangle ADE is similar to triangle ABC.

Triangle ABC is isosceles.

Angle A is equal to 30°.

Calculate the size of angle E.

Video Solution

Answer

$75\degree$

Exercise #3

Triangle ADE is similar to triangle ABC.

Triangle ABC is isosceles.
Angle A is equal to 40°.

Calculate angle D.

Video Solution

Answer

$70\degree$

Exercise #4

Triangle ADE is similar to isosceles triangle ABC.

Angle A is equal to 60°.

Calculate angle E.

Video Solution

Answer

$60$

Exercise #5

Triangle ADE is similar to equilateral triangle ABC.

Angle A is equal to 20°.

Calculate angle D.

Video Solution

Answer

$80$

Question 1

Triangle DEF is congruent to triangle ABC.

Angle B is equal to 60°.

Angle C is equal to 35°.

What is the size of angle D?

Question 2

Triangle DEF is congruent to triangle ABC.

Angle A is equal to 60°.

Angle B is equal to 70°.

What is the size of angle F?

Question 3

Triangle DEF is congruent to triangle ABC.

Angle D is equal to 45°.

Angle F is equal to 65°.

What is the size of angle B?

Question 4

Triangle DEF is congruent to triangle ABC.

Angle A is equal to 70°.

Angle C is equal to 55°.

What is the size of angle E?

Question 5

Triangle DEF is congruent to triangle ABC.

Angle B is equal to 60°.

Angle C is equal to 75°.

What is the size of angle D?

Exercise #6

Triangle DEF is congruent to triangle ABC.

Angle B is equal to 60°.

Angle C is equal to 35°.

What is the size of angle D?

Video Solution

Answer

$85$ °

Exercise #7

Triangle DEF is congruent to triangle ABC.

Angle A is equal to 60°.

Angle B is equal to 70°.

What is the size of angle F?

Video Solution

Answer

$50$ °

Exercise #8

Triangle DEF is congruent to triangle ABC.

Angle D is equal to 45°.

Angle F is equal to 65°.

What is the size of angle B?

Video Solution

Answer

$70$ °

Exercise #9

Triangle DEF is congruent to triangle ABC.

Angle A is equal to 70°.

Angle C is equal to 55°.

What is the size of angle E?

Video Solution

Answer

$55$ °

Exercise #10

Triangle DEF is congruent to triangle ABC.

Angle B is equal to 60°.

Angle C is equal to 75°.

What is the size of angle D?

Video Solution

Answer

$45$ °