Question

Find the values of x and y in the given triangles where ∠A = 70°, ∠B = 36°, ∠D = 68° and ∠F = 56°.

Answer 1

Given:

We have two triangles likely connected or corresponding:

△ABC with ∠A = 70°, ∠B = 36°

△DEF with ∠D = 68°, ∠F = 56°

We are asked to find x and y likely unknown angles in the triangles

Step 1: Use the sum of angles in a triangle

The sum of angles in a triangle is always 180°.

Triangle ABC:

∠A + ∠B + ∠C = 180°

70 + 36 + x = 180°

106 + x = 180°

x = 180 – 106°

x = 74°

Likely, x corresponds to the exterior angle at vertex C:

Exterior angle x = 180 – ∠C

= 180 – 74

= 106°

Triangle DEF:

∠D + ∠F + ∠E = 180°

68 + 56 + y = 180°

124 + y = 180°

y = 56°

Again, if y is the exterior angle, then: y = 180 − 56 = 124°

Maybe y corresponds to the angle at vertex E, the remaining interior angle:

y = 180 – (∠D + ∠F)

= 180 – 68 – 56

= 56°

Maybe the diagram makes y opposite or exterior:

Exterior angle = 180° – opposite interior angle

If angle at vertex E = 56° opposite, then y = 180 – 56 = 124°

Alternatively, perhaps the given problem interprets y = 86° using another configuration like a quadrilateral formed by the two triangles.