Question

Can you solve please

Answer 1

y = 10

∡C = 40°

∡D = 76°

Explanation:

Supplementary angles sum 180°

116° and ∡E are supplementary angles:

116 + E = 180°

E = 180 - 116

E = 64°

∡E = 64°

Internal angles of a triangle sum 180°

∡D + ∡C + ∡E = 180°

7y+6 + 4y + 64 = 180

7y + 4y + 6 + 64 = 180

11y + 70 = 180

11y = 180 - 70

11y = 110

y = 110/11

y = 10

Then:

∡C = 4y = 4*10 = 40°

∡D = 7y + 6 = 7*10 + 6 = 70 + 6 = 76°

Answer 2

y = 10 , ∠ C = 40° , ∠ D = 76°

Explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ DEF is an exterior angle of the triangle , then

∠ C + ∠ D = ∠ DEF , that is

4y + 7y + 6 = 116

11y + 6 = 116 ( subtract 6 from both sides )

11y = 110 ( divide both sides by 11 )

y = 10

Then

∠ C = 4y = 4(10) = 40°

∠ D = 7y + 6 = 7(10) + 6 = 70 + 6 = 76°