In triangle δabc, ∠c is a right angle and cd is the height to ab find the angles in δcbd and δcad if: m∠a = 65°

In triangle ΔABC,

<C= 90°    ( Given angle is is a right angle).

m∠A = 65°    (Also given).

Sum of angles of a triangle is 180°.

We can set an equation for angles A, B and C.

<A+<B+<C = 180°.

Plugging values of <A and <C in above eqaution.

90° + <B + 65° = 180°

<B + 155 = 180.

Subtracting 155 from both sides.

<B +155 - 155 = 180-155.

<B = 25°.

Therefore, <B = 25°.

Now, in triangle ΔCBD.

<D = 90°.                      (Give CD is perpendicular to AB. A perpendicular line subtands an angle 90 degrees).

< B= 25°                        ( We found above).

Now, sum of angles of triangle ΔCBD is also 180 degree.

We can setup another equation,

<B + <D + < BCD = 180 °.

Plugging values of B and D in above equation.

25 + 90 + <BCD = 180.

115 + < BCD = 180.

Subtracting 115 from both sides.

115 + < BCD -115 = 180-115.

<BCD = 65°.

Now, in triangle ΔCAD.

<D = 90°.

<A = 65°

We need to find <ACD.

Now, sum of angles of triangle ΔCAD is also 180 degree.

We can setup another equation,

<A + <D + < ACD = 180 °.

65 + 90 + <ACD = 180.

155 + <ACD = 180.

Subtracting 155 from both sides.

<ACD +155 - 155 = 180-155.

<ACD = 25°.

Therefore, <ACD= 25°, <BCD = 65°, <D=90°, <B= 25°.

In triangle CBD

In triangle CAD

Step-by-step explanation:

In triangle ABC

We know that sum of angles of a triangle =180 degrees

By using substituting property of equality

By subtraction property of equality

In triangle CBD

Because CD is perpendicular to AB.

By substitution property

By subtraction property of equality

In triangle CAD

Because CD is perpendicular to AB.

By using substitution property

By subtraction property of equality

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step-by-step explanation: