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In this paper, we mainly discuss the angle modulus of convexity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>δ</mi><mrow><mi>X</mi></mrow><mi>a</mi></msubsup><mrow><mo>(</mo><mi>ϵ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and the angle modulus of smoothness <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>ρ</mi><mrow><mi>X</mi></mrow><mi>a</mi></msubsup><mrow><mo>(</mo><mi>ϵ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> in a real normed linear space <i>X</i>, which are closely related to the classical modulus of convexity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>δ</mi><mi>X</mi></msub><mrow><mo>(</mo><mi>ϵ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and the modulus of smoothness <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>ρ</mi><mi>X</mi></msub><mrow><mo>(</mo><mi>ϵ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Some geometric properties of the two moduli were investigated. In particular, we obtained a characterization of uniform non-squareness in terms of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>ρ</mi><mrow><mi>X</mi></mrow><mi>a</mi></msubsup><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. Meanwhile, we studied the relationships between <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>δ</mi><mrow><mi>X</mi></mrow><mi>a</mi></msubsup><mrow><mo>(</mo><mi>ϵ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>ρ</mi><mrow><mi>X</mi></mrow><mi>a</mi></msubsup><mrow><mo>(</mo><mi>ϵ</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> and other geometric constants of real normed linear spaces through some equalities and inequalities. Moreover, these two coefficients were computed for some concrete spaces.